High-Q Low-Impedance MEMS Resonators

Transcription

Li-Wen Hung
Clark Nguyen
Electrical Engineering and Computer Sciences
University of California at Berkeley
Technical Report No. UCB/EECS-2012-218
http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-218.html
December 1, 2012
Copyright © 2012, by the author(s).
All rights reserved.
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permission.
Acknowledgement
I am indebted to Prof. Nguyen for his generous support and guidance. I
would like to thank Prof. King Liu and Prof. Lin for serving on my qualifying
exam and dissertation committees, as well as Prof. Alon for serving on my
qualifying exam committee. Prof. Bhave (Cornell U.), Prof. Gianluca Piazza
(U. of Pennsylvania), Prof. Pisano and Prof. Javey, Dr. Justin Black and Dr.
Philip Stephanou (Qualcomn). They have provided me timely help when I
needed them and valuable feedback to better my research.
I thank my current group members for their friendship and technical
supports. I thank all of the BSAC directors and researchers for their
endless efforts to make BSAC an even better environment for graduate
students to learn and to grow professionally.
The deepest thanks go to my family.
by
Li-Wen Hung
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Engineering-Electrical Engineering and Computer Sciences
in the
Graduate Division
of the
University of California, Berkeley
Committee in charge:
Professor Clark T.-C. Nguyen, Chair
Professor Tsu-Jae King Liu
Professor Liwei Lin
Spring 2011
Copyright © 2011
by
Li-Wen Hung
Abstract
by
Li-Wen Hung
Doctor of Philosophy in Engineering – Electrical Engineering and Computer Sciences
University of California, Berkeley
Professor Clark T.-C. Nguyen, Chair
The ever increasing need for regional and global roaming together with continuous advances
in wireless communication standards continue to push future transceivers towards an ability to
support multi-mode operation with minimal increases in cost, hardware complexity, and power
consumption. RF channel-select filter banks pose a particularly attractive method for achieving
multiband reconfigurability, since they not only provide the needed front-end reconfigurability,
but also allow for power efficient and versatile transceiver designs, e.g., software-defined radio.
Such channel-select filters, however, impose requirements on their constituent resonators that are
not yet achievable on the micro-scale. Specifically, capacitively-transduced micromechanical
resonators achieve high Q, but suffer from high impedance; while piezoelectric micromechanical
resonators offer low impedance, but with insufficient Q. This dissertation demonstrates four new
techniques to address the issues in both technologies.
Two of the methods recognize that sub-30 nm gap spacing enables electrostatic resonators to
achieve acceptably low impedance. Unfortunately, however, such small gaps with the needed
high aspect ratios are difficult to achieve via wafer-level batch processing. Two new methods are
proposed and experimentally verified for forming sub-30 nm gaps: 1) partial-filling of electrodeto-resonator gaps with atomic layer deposition (ALD) of high-k dielectric; and 2) generating
gaps via the volume reduction associated with a silicidation reaction. Among the many benefits
provided by a silicide-based approach to gap formation is speed of release, where sub-30 nm
gaps can be formed and high-aspect-ratio microstructures can be released via anneals lasting
from seconds to a few minutes, regardless the lateral dimensions of the devices. Silicide-induced
gap formation further does not require any etching and is applicable to a wide range of
applications, from electronics to vacuum packaging.
The next two methods seek to circumvent the fact that AlN thin-film resonators have
historically been measured with much lower Q than capacitive ones at similar frequencies. As a
result, it was commonly accepted that the AlN thin films sputtered at low temperatures are to
blame for the lower Q. This dissertation provides experimental evidence that it is not AlN
material loss that restricts the Q‟s of conventional AlN resonators, but rather the losses
associated with their contacting electrodes. Specifically, a new transducer dubbed the
1
“capacitive-piezoelectric” transducer is introduced that lifts the electrodes away from a
piezoelectric resonator by tiny nanometer scale gaps that retain strong electric fields for good
electromechanical coupling, while eliminating electrode-derived losses. After removing the
electrode losses, the Q‟s of piezoelectric AlN resonators rise by up to 9 times. A new surfacemicromachining fabrication process has been developed for the capacitive-piezoelectric
resonators, where the metal electrodes are separated from the AlN resonators by small air (or
vacuum) gaps. The second approach for tapping the material Q of AlN uses Q-boosting
mechanical circuits, where the electrode-equipped AlN resonators are mechanically coupled to
electrode-less ones to form a composite-array. In this structure, the energy shared among all of
the resonators in the composite-array effectively „boost‟ the Q‟s of the electrode-equipped
resonators. The Q of electrode-less resonators are extrapolated from the measurement data to be
from 14,040 to 15,795. Both methods achieve measured Q‟s exceeding 10,000, posting the
highest reported Q‟s for resonators constructed of sputtered AlN and confirming that AlN is
indeed a high-Q material.
__________________________________
Professor Clark T.-C. Nguyen
Committee Chair
2
To my parents and my brother.
i
Table of Contents
Chapter 1: Introduction
1.1
1.2
1.3
1.4
1.5
1.6
Characterization of Multi-Standard Receivers ………………………........1
Narrow-Band MEMS Filters ………………………………………….......4
1.2.1 Fundamentals of Micromechanical Resonators …………………..4
1.2.2 Modeling of Micromechanical Couplers …………………………6
1.2.3 Transfer Functions of Mechanical Circuits ……………………….7
1.2.4 Quarter-Wavelength Couplers for MEMS Filters …………….......9
1.2.5 Half-Wavelength Couplers for Composite-Array Resonators …..10
1.2.6 Filter Termination ……………………………………………….12
1.2.7 Filter FOM ………………………………………………………13
1.2.8 Filter Insertion Loss ……………………………………………..16
Previous Work on Capacitive MEMS Resonators ………………………18
1.3.1 Single-Crystal Silicon Capacitive Resonators …………………..18
1.3.2 Poly-Si and Poly-SiGe Capacitive Resonators ………………….18
1.3.3 Metal Capacitive Resonators …………………………………....18
1.3.4 Other Materials ………………………………………………….19
Previous Work on Piezoelectric MEMS Resonators ……………………20
1.4.1 SAW Resonators ………………………………………………...20
1.4.2 FBAR and BAW Resonators …………………………………....20
1.4.3 Lateral-Mode Thin-Film AlN Resonators ……………………....20
Thesis Outline …………………………………………………………...21
References ……………………………………………………………….22
Chapter 2: ALD Partially-Filled Gaps
2.1
2.2
2.3
2.4
Introduction ……………………………………………………………...25
Coupling Efficiency of Capacitive Resonators ………………………….25
2.2.1 Capacitive Transducers ………………………………………….25
2.2.2 Filter FOM of Capacitive Resonators …………………………...27
Gap Reduction via Partial Gap Filling …………………………………..29
2.3.1 Methods for Achieving Small Gaps ……………………………..29
2.3.2 ALD Partial-filling for Sub-50nm Gap Spacing ………………...30
2.3.3 Atomic Layer Deposition (ALD) ………………………………..31
Experimental Results ……………………………………………………33
2.4.1 Wine-Glass Disk Resonators ……………………………………33
2.4.2 Extrapolation of Gap Spacing Before and After ALD …………..35
2.4.3 Extrapolation of Interconnect Resistance ……………………….38
2.4.4 Measurement Results – Improved FOM ………………………...40
ii
Methods for Restoring Q ………………………………………..42
a. Annealing …………………………………………………....42
b. Remove Undesired HfO2 Films ……………………………..46
c. Reduce Surface Loss via Barrier Layer ……………………..46
d. Reduce Surface Loss via Smoother Surface ………………...47
2.4.6 Dielectric Charging ……………………………………………...47
References ……………………………………………………………….49
2.4.5
2.5
Chapter 3: Silicide-Induced Gaps
3.1
3.2
3.3
3.4
3.5
Fabrication of High Aspect Ratio microstructures ……………………...52
3.1.1 Need for High Aspect Ratio Microstructures …………………...52
3.1.2 Wafer Bonding …………………………………………………..52
3.1.3 Direct Dry Etching ……………………………………………....53
3.1.4 Release by Etching Sacrificial Materials ………………………..54
Silicide-Induced Gaps …………………………………………………...55
3.2.1 Better Ways for Forming Internal Gaps …………………………55
3.2.2 A Brief Introduction to Silicidation ……………………………..56
3.2.3 Silicide-Induced Gaps …………………………………………...58
Experimental Results ……………………………………………………59
3.3.1 Demonstration of Silicide-Induced Gaps ………………………..59
3.3.2 Repeatability …………………………………………………….60
3.3.3 Operational Temperature Range ………………………………...63
3.3.4 Small Gaps and Lateral Gaps ……………………………………63
3.3.5 CMOS Compatibility ……………………………………………64
3.3.6 Released Microstructures ………………………………………..65
3.3.7 Released Titanium Beam Resonators …………………………...67
Conclusions and Future Work …………………………………………..69
References ……………………………………………………………....70
Chapter 4: Capacitive-Piezoelectric Resonators
4.1
4.2
4.3
4.4
Raising Q of Piezoelectric Resonators …………………………………..73
Capacitive-Piezoelectric Transducers …………………………………...75
Analytical Modeling …………………………………………………….77
4.3.1 Electromechanical Coupling Coefficients ………………………77
4.3.2 Frequency Shift and k2eff ………………………………………...84
4.3.3 Linearity (PIIP3)…………………………………………………..86
Fabrication Process ……………………………………………………...89
4.4.1 Overall Fabrication Flow ………………………………………..89
4.4.2 Characterization of Lift-Off Process …………………………….94
4.4.3 AlN and Metal Sputtering ……………………………………….98
4.4.4 AlN and Molybdenum Dry Etching ……………………………..99
4.4.5 Nickel Electroplating …………………………………………..101
4.4.6 XeF2 Release …………………………………………………..104
4.4.7 Final Remarks on Fabrication …………………………………105
iii
4.5
4.6
4.4.8 Fabricated Devices …………………………………………......105
Electrical Measurements ……………………………………………….107
4.5.1 1.2 GHz Contour-Mode Ring Resonators ……………………...107
4.5.2 50 MHz Wine-Glass Resonator Array …………………………108
References ……………………………………………………………...113
Chapter 5: Q-Boosting AlN Array-Composite
5.1
5.2
5.3
5.4
5.5
Introduction ………………………………………………………….…116
Q-Boosting Micromechanical Circuits ………………………………...117
5.2.1 Array-Composite of identical Resonators ……………………...118
a. Energy Analysis ……………………………………………118
b. Equivalent Circuit Analysis ………………………………..119
5.2.2 Coupling Resonators of Various Sizes.………………………...121
5.2.3 Variations in Coupling Locations ……………………………...126
Experimental Results …………………………………………………..127
5.3.1 Fabrication of AlN Q-Boosted Composite-Array ……………...127
5.3.2 Electrical Measurements ……………………………………….134
Conclusions …………………………………………………………….138
References ……………………………………………………………...138
Chapter 6: Conclusions
6.1
6.2
6.3
Achievements …………………………………………………………..140
Future Research Directions …………………………………………….142
References ……………………………………………………………...143
iv
Acknowledgements
I am indebted to Prof. Clark Nguyen for his generous support and guidance. He transferred
me to UC Berkeley after I failed to find a Ph.D. advisor and any funding in the University of
Michigan. I have been enjoying doing research with him since then. Later on I started to receive
research awards and I thanked him each time. He indeed gave me a chance when I needed it the
most, and for that alone, I will forever be grateful. For the past four years, he gave me a lot of
freedom to explore what interested me and supported what I eventually decided to do; he did not
lose his confidence in me even after my fabrication failed to work for the entire year. His
constant trust and patience for me inspired me to achieve more.
I would like to thank Prof. Tsu-Jae King Liu and Prof. Liwei Lin for serving on my
qualifying exam and dissertation committees, as well as Prof. Elad Alon for serving on my
qualifying exam committee. Prof. Sunil Bhave (Cornell University), Prof. Gianluca Piazza
(University of Pennsylvania), Prof. Albert Pisano and Prof. Ali Javey (UC Berkeley), Dr. Justin
Black and Dr. Philip Stephanou (Qualcomn). They have provided me timely help when I needed
them and valuable feedback to better my research.
I have no idea how the staff of Berkeley Microlab/Nanolab manages to handle a lab filled
with tools with chronic disease and naive users who tend to make unintentional mistakes (I was
one of them). I can only imagine and appreciate the efforts and patience it takes to maintain such
a dynamic, almost chaotic, lab. I am especially thankfully to Dr. XiaoFan Meng, Joe Donnelly,
and Jimmy Chang, who shared with me valuable knowledge in microfabrication and mechanics.
I had no fabrication experience before I started my Ph.D. studies and no senior student to follow
but could still function in the lab, thanks to the generous help from many Microlab members,
especially Zach Jacobson, Jason Tien, and Reinaldo Vega. I will miss being surrounded by
friends when working in the clean room and the fun we had there.
I thank my current group members for their friendship and technical supports. Their efforts
have made our testing lab space organized and convenient. Most of my close friends in Berkeley
and the professional connections came through BSAC. I always enjoy the good people and good
food during each BSAC IAB meeting, and I am proud to be part of BSAC. I thank all of the
BSAC directors, John Huggins, Richard Lossing, and Kim Ly for their endless efforts to make
BSAC an even better environment for graduate students to learn and to grow professionally.
The deepest thanks go to my family. My parents showed me how resilience and hard working
can make a difference in the end. My father is a wonderful physics teacher and I hope I will turn
out to be his best student. During my Ph.D. studies, my brother was also pursuing his Ph.D.
degree in mechanical engineering. We explored the unknown together as kids and I am always
proud to be the little sister of this smart guy. Science and technology started to endear me at the
dinner table twenty years ago and the passion eventually leads me to where I am now.
I am in great debt to my fiancé, Reinaldo Vega, yet another engineer. We spent more time
together in Cory 373 and Berkeley Microlab than anywhere else for the past four years. We
challenged each other’s research yet encouraged and supported each other’s ambition and
passion like no one else. He has made my thousands of 12-hour long working days delightful and
continues to inspire me with his generosity for the unprivileged. To me, he is the major award.
I am privileged to receive enormous support and encouragements from many capable and
wonderful people, who want me to succeed. That realization, along with my own passion, will
continue to drive myself to accomplish and to contribute.
v
Chapter 1: Introduction
1.1 Channelization of Multi-Standard Receivers
With increasing need for the regional and global roaming of transceivers and continuous
advances on wireless communication protocols, future transceivers need flexibility across
various mobile communication standards and environments. To understand the design challenge,
it is instructive to first review a conventional receiver of heterodyne architecture shown in Fig. 11. This receiver relies on multiple frequency-dependent passive components, such as dielectric or
bulk-acoustic wave (BAW) filters for RF band selection and surface acoustic wave (SAW) filters
in the IF stage. For the past decade, RF MEMS has emerged as a potential solution for
miniaturization of transceivers by replacing the bulky off-chip components with on-chip and
small-sized MEMS components [1][2].
The center frequencies and the passband width of these frequency-dependent filters can be
fine-tuned via applications of mechanical strain [3], electric DC voltages to ferroelectric material
[4], piezoelectric material [5], electrostatic transducers [6], and thermal stress [7]. However, it
proves very difficult, if possible, to extend the tunable range of filter passband to cover all the
commercially available communication standards, roughly from 900 MHz to 5 GHz. The most
intuitive way to achieve a transceiver that can support multiple communication standards is to
switch among multiple transceivers corresponding to each standard. Even with the help of smallsized MEMS components, such a brute force approach is not cost-effective with the
overwhelming hardware count and complexity of the system.
With the rapid advances in computing power enabled by aggressive scaling of CMOS
technology, there is a steady trend towards using digital circuits to assist the analog circuits or to
replace them. Following this trend, software defined radio (SDR) has been proposed to expand
the digital processing from baseband towards the antenna, replacing analog front-ends with
digital ones [8]. As hardware for digital signal processing is inherently reconfigurable and
RF Band
Selection Filter
Image-Reject
Filter
IF Channel
Selection Filter
I
90˚
Q
LO
Signal
I-Q
Osc.
Quartz
Xstal
Fig. 1-1 Super-heterodyne receiver with off-chip band selection radio-frequency (RF) filter,
image-reject filters, and intermediate-frequency (IF) channel selection filter, quartz crystal as the
source of frequency reference.
1
versatile, SDR is promising for a flexible transceiver that can operate under any available
standard within commercial communication RF bands (from 0.9 GHz to 5 GHz).
An ultimate SDR (i.e., use as minimum analog components as possible) shown in Fig. 1-2(a)
digitizes the entire receiving RF band right after the antenna or after a wideband low-noise
amplifier (LNA) via an analog-to-digital converter (ADC). Such an ADC needs to operate at
multiple GHz to fulfill the Nyquist criterion across the entire receiving band (e.g., sample rate of
12 Gigabytes per second to accurately digitalize RF signals up to 6 GHz). On the other hand,
without any RF filtering, the ADC has to cope with high dynamic range of the received signals.
For example, the Global System for Mobile Communications (GSM) requires an RF front-end
dynamic range as high as ~100 dB with signal in the vicinity. In principle, the dynamic range of
memory-less ADCs can rise by 3 dB per doubling the oversampling ratio and by 6 dB per
additional bit of quantization resolution. Given this trend, 100 dB dynamic range is not
achievable with practical power consumption. For example, the work in [9] achieves 2 bits
resolution at 4 GS/s (giga-samples per second) operation and 34 mW power using 180 nm
CMOS and 1.8 V power supply; the work in [10] achieves 5 bits resolution at effectively 1.75
GS/s operation and 7.6 mW power using 90 nm CMOS and 1 V power supply; the work in [11]
achieves 6 bits resolution at 5 GS/s operation and 320 mW power using 65 nm CMOS and 1.3 V
power supply. The low-power realization of ADC‘s with operation speed exceeding 1 GS/s and
quantization resolution larger than 10 bits remain elusive.
To avoid the above problem, alternatively, received signals are first down-converted to zero
IF or low IF with harmonic-suppression mixing via multi-phased local oscillators (LO) [12][13]
before digitization, shown in Fig. 1-2(b). This architecture facilitates the ADC design but puts
challenges on the mixer design. In particular, the need for large tuning range of LO signals to
Wideband
LNA
Anti-Aliasing
Filter
ADC
Wideband
LNA
Digital
Front-End
DSP
Data
Digital
Front-End
DSP
Data
Anti-Aliasing
Filter
ADC
LO
Signal
Fig. 1-2: (a) Block diagram of ultimate software-defined radio (SDR), where a wideband antenna
and wideband low-noise amplifier (LNA) receive all the signals reside in the RF commercial
band, followed by ADC and digital circuits. Here, ADC needs to operate at multiple GHz
frequency with high dynamic range. (b) Feasible SDR with frequency down-conversion before
ADC. Without pre-filtering, phased local-oscillation signal is required for an interference robust
design.
2
cover the entire receiving RF band and highly linear mixers operating at RF frequency range
impedes further reduction of power consumption down to < 1 mW range.
Note that the high dynamic range and interference-resistant requirements are a direct result of
wide-band reception for narrow-band signals such as GSM, in which each channel is only 200
kHz wide. Selection of the entire receiving band, e.g., 25 MHz for GSM at 900 MHz, usually
will include not only the single in the target channel but also all the signals in the other channels
within the receiving band, i.e., interferences. Given the same target single power level, the wider
the receiving band, the more inferences likely to exist. This is especially a problem for receivers
designed to operate by multiple standards by using a wideband LNA shown in Fig. 1-2(b).
On the other hand, when signals of various communication standards can be selected directly
from the targeted channel by filters of appreciate passband widths, as shown in Fig. 1-3 [1], the
dynamic range requirement of the following circuits remains similar to a single standard
receiver, regardless the total operational receiving band width covered by the receiver. Such
approach requires a bank of narrow-band filters, each designed for a receiving channel. Indeed,
the current trend of SDR architecture design remains to avoid analog RF filtering altogether
stems from the fact that today‘s off-chip filters are bulky and expensive compared to digital
circuits. For the same reason, conventional analog filters are not suitable for a cost and area
effective implementation of the filter bank in a channel-selection receiver in Fig. 1-3. MEMS
filters are one of the most promising solutions for such filter bank.
Before the design principals of MEMS narrow-band filters are presented, it is illustrative to
first look at the parameters commonly used to evaluate filter performance shown in Fig. 1-4. Of
special interest is the filter insertion loss and 20 dB filter shape factor. Insertion loss is measured
as the difference in loss between a through measurement (i.e., by replacing the filter with a
highly conductive metal strip on the chip or PCB board in the measurement setup) and a
measurement after the filter has been inserted. 20 dB filter shape factor is the ratio between the 3
dB-bandwidth to the 20dB-bandwidth. 20 dB filter shape factor describes how sharp the filter
ADC
Digital
Baseband
LNA
Filter
Bank
Fig. 1-3: channel-selection RF filters reject all the interference signals and allow the receiver to
operate with relaxed dynamic range requirements, simplified circuits, and lower power
consumption.
3
passband is.
The rest of this chapter briefly reviews the design of narrow-band filters to illustrate the
performance requirements posted on the constituent MEMS resonators, followed by reviews on
previous work using both electrostatic and piezoelectric resonators. This thesis sets out to
address the current challenges of implementing MEMS resonators suitable for synthesizing such
narrow-band MEMS filters.
1.2 Narrow-Band MEMS Filters
The basic circuit modeling of resonators and mechanical coupling beams is presented here as
background knowledge for narrow-band filter design.
1.2.1 Fundamentals of Micromechanical Resonators
A MEMS resonator consists of a resonant mechanical structure and transducers for energy
conversion between electrical and mechanical domains, shown in Fig. 1-5. The resonant
mechanical structures, regardless of whether their shapes are that of beams, disks, rings, or
plates, can all be modeled as spring-mass-damper systems. The equivalent mass at any given
point of the resonator is determined from the total kinetic energy of the resonator KEtot and the
velocity at that point v(x,y), as given by [15]
2 KEtot
2H

 ( x , y )  v( x , y ) 2 dxdy
2
2
A
v( x , y)
v( x , y)
2H

 ( x , y )  ( x , y ) 2 dxdy
2
( x , y) A

mre 
(1-1)

S21 (dB)
0 dB
Insertion Loss
3 dB
Filter
Bandwidth
20 dB
20 dB
Bandwidth
Frequency
Fig. 1-4: Parameters commonly used to evaluate filter performance.
4
Force(F)
Input
Transducer
Input
voltage
(vi)
i  F
Displacement (x)
Vibrating
Resonator
vi
1:η i
 o   i  io
ηo:1
1/kr
mr
cr
Output
Transducer
x
Output
Current
(io)
io
vo
vi
Co2
Co1
Vibrating Mechanical Structures:
Disk
Ring
Plate
Beam
vo
vi
RL
Higher Q
Lower Q
fo
Fig. 1-5: (a) block diagram of a MEMS resonator consisting of electro-mechanical transducers
and vibrating mechanical structures, and (b) a general electric model for a MEMS resonator.
where H, ρ(x,y) and Φ(x,y) are the thickness, density, and vibration mode shape of the resonator.
The effective stiffness of the resonator kre can be related to mre via the radian resonance
frequency ωo
kre  o2 mre
(1-2)
Finally, the value of the damping element is related to mass, stiffness, and the Q of the
resonator, by
c re 
kre mre
Q

 o mre
Q
(1-3)
To the first order, a micromechanical resonator can be modeled by the electrical circuit in
Fig. 1-5 regardless of the geometry, mode shape, and transduction methods. The values of
inductance, capacitance, and resistance correspond to values of equivalent mass mre, reciprocal
of stiffness, 1/kre, and damping factor cre. The two physical capacitors, Co1 and Co2, represent the
total capacitance contributed by the transducers and parasitic capacitance at the input or output
ports. The transduction coefficients, ηi and ηo, model energy transduction efficiency between
electrical and mechanical domains by considering the amount of mechanical force F generated
5
from voltage input vi and the output current io generated from mechanical displacement x,
respectively:
i 
F
vi
 o  o
io
x
(1-4)
The simplified model presented here intends to prepare readers for the following filter
design. More details on design of capacitive and piezoelectric resonator designs will be presented
in Chapter 3 and Chapter 5, respectively.
The electro-mechanical transducer in the input port converts input electrical energy (i.e.,
voltage) to mechanical energy (i.e., strain or stress). On the output port, the transducer converts
the mechanical energy (i.e., displacement) back to electric energy (i.e., output currents). The
efficiency of such energy transduction is quantified by electromechanical coupling coefficient, η,
and is modeled by the turn ratios of the transformers on the input and output ports, respectively.
A filter can be implemented by a system of the degree of freedom larger than one. For
example, two resonators mechanically coupled to each other together form a two-pole filter. To
understand the mechanical circuit design from the perspective of equivalent electrical circuit
design, it is instructive to first be familiar with the electrical circuit model for a coupling beam
with a resonator attached to each end.
1.2.2 Modeling of Micromechanical Couplers
The micromechanical coupling beams connected between resonators function as acoustic
transmission lines. The coupling beam in consideration has cross-sectional dimensions of width
Wc and height Hc, shown in Fig. 1-6(a) and vibrates in the extensional mode shape, i.e., the beam
expands and contracts along the length of the beam Lc. It can be modeled by the T-shaped
capacitor combination [14][15] shown in Fig. 1-6(b) with the impedance value of each capacitor
written as:
Za  Zb 
Zc 
cos2  Lc / c   1
jZ o sin2  Lc / c 
(1-5)
1
jZ o sin2   n 
(1-6)
with Zo and λn being the normalized impedance and normalized wavelength, respectively
Zo 
c 
1
H cWc E
E 
fo
ve

fo
(1-7)
(1-8)
where E and ρ are the Young‘s modulus and density of the resonator structural material,
6
respectively, and fo is the resonant frequency.
1.2.3 Transfer Functions of Mechanical Circuits
Fig. 1-7 shows a mechanical circuit composed of two contour-mode disk resonators
mechanically coupled to each other with resistors RQ connected to both the input and the output
ports. Fig. 1-7(b)-(c) show its equivalent mechanical and electrical circuits, respectively.
The transformer turns ratios associated with the couplers in Fig. 1-7(c), ηc1 and ηc2, model the
mechanical impedance transformation realized by mechanically coupling one resonator to the
other at a location different from the reference point based on which the electrical models of each
resonator is calculated. Usually the reference point is chosen as the location with the maximum
mechanical displacement. Expressed in terms of a stiffness ratio, the equation for the mechanical
transformer turns ratio when coupling at a distance from an anchor takes the form [16]
c 
krc
kre
(1-9)
where krc is the resonator stiffness at the coupling position and kre is the equivalent stiffness as
derived in (1-2). Note that when ηc1 and ηc2 have equal values, they only modify the values of Za,
Zb, and Zc, and have no effect on the other circuit elements. Such coupling has been utilized in
filters to obtain smaller bandwidth [17]. As will be seen, such coupling will be required when
implementing filters with two or more resonators.
To simplify the analysis, the circuit in Fig. 1-7(c) is reduced to (d) by absorbing all of the
transformer ratios, ηi, ηo , ηc1 , and ηc2, into the values of the circuit elements, yielding
Lx  mr /  i o
(1-10)
C x   i o / k r
(1-11)
Rx  c r /  i o
(1-12)
C ca  C cb   i o c 1 c 2 / kca
(1-13)
C cc   i o c 1 c 2 / kcc
(1-14)
As the mechanical circuit in Fig. 1-7(a) is a system of two degrees of freedom, a 2-rank
matrix equation can fully describe its equivalent circuit in Fig. 1-7(d):


1
1 
1



  
  i1 
sC sa sC sc 
sC ss

    vin 
 


1
1
1     v1 
  
   i2 



sC ss
sC sa sC sc   


7
(1-15)
where δ is the impedance of each resonator in the array and is a function of frequency
  sLx 
1
 Rx
sC x
(1-16)
It is worth noting that solving this matrix to obtain output current given applied voltage is
equivalent to solving the vibration velocity, i.e., time derivation of vibration amplitude x, given
applied force of a two-degree freedom coupled mechanical system, as shown in Fig. 1-7(b):
 s 2 mr  sc r  kr  k sa  k sc

 k sc

 x1 
    F1 
 

s 2 mr  sc r  kr  k sa  k sc     F2 
 x 2 
 k sc
(1-17)
where (1-17) is related to (1-15) with the relation
i x
x
 s
v F
F
(1-18)
The current-to-voltage relationship of the circuit in Fig. 1-7(d) can be obtained by solving (115) as
i1

v1 
 


1 
1
1

1  sC sc   


sC sa 
sC sa sC sc


1 
1
2 

1 
1   
  


  SC sc   
  2   

sC sa 
sC sa sC sc 
sC sa  
sC sa   

(1-19)
1
sC sc
i2
1


v1 
1 
1
2 

1 
1   
  


  
  SC sc   
  2   
sC sa 
sC sa sC sc 
sC sa  
sC sa   


(1-20)
Lc
Zca
v1
Hc
i1
Zcb
Zcc
i2
v2
(b)
Wc
Fig. 1-6: (a) dimension of a coupling beam to vibrate in the extensional mode shape along its
length Lc. (b) Equivalent T-shaped capacitor combination model for the coupling beam, where
Zca and Zcb share the same value. The equivalent wavelength of the coupler governs the ratio of
Zca to Zcc.
(a)
8
where i1 and i2 represent the output currents generated by the first and the second resonators,
respectively. The values of Csa and Csc are not independent and the ratio is a function of the
length of the extensional-mode coupling beams. Of particular interest are cases when the length
is equivalent to quarter and half wavelength, as discussed the following two sections.
1.2.4 Quarter-Wavelength Couplers for MEMS Filters
For extensional mode coupling beams of length designed to be integer number of quarterwavelength coupler, i.e., Lc/λn=N±0.25, N=1, 2,…, equations (1-5) and (1-6) yields to the
relation
Za  Zb   Zc
(1-21)
C ca  C cb  C cc
(1-22)
or
io
Rs
vo
vi
Rs
VP
(a)
kc12a
kr1
cr1
(b)
kc12c
kr2
mr2
cr2
F1
Rs
vi
mr1
kc12b
1:ηi
mr 1/kr
cr
1:ηc1 1/kca
Co
1/kcb η :1
c2
mr 1/kr
cr
ηo:1 io
vo
Co
1/kcc
Rs
(c)
Rs
vi
(d)
Le
Ce
Re
Cca Ccb
Co
Ccc
Le
C e Re
io
vo
Co
Rs
Fig. 1-7: (a) An un-terminated MEMS filter composed of two identical disk resonators, one of
which is the input resonator and the other is the output resonator; (b) mass-stiffness-damper
model of the filter in (a); (c) equivalent electrical circuit of the filter in (a); (d) a simplified
version of the circuit in (c).
9
Plugging (1-21) and (1-22) to (1-19) and (1-20) yields
i1

0.5
0.5



1
v1 
1 
1   1

  
  

sC sa
sC sa
sC sa 
sC sa 

(1-23)
1
sC sc
i2
 0.5
0.5



1
1
v1 
1 
1  

  
  

sC sa
sC sa
sC sa 
sC sa 

(1-24)
Each term in (1-23) and (1-30) takes the mathematical form of resonator response, where the
resonant frequency is different from fo through addition or subtraction of Csa to or from the
motional capacitor of the constitute resonator, Cr. The magnitudes of the output currents
therefore show peak values at two frequencies, fo+∆f and fo-∆f, respectively. The magnitude of
∆f/fo (i.e. percentage of frequency change relative to the center frequency fo) is
f
C
 1 r 1
fo
C ca
(1-25)
As will be shown in Section 1.3.4, a filter response with center frequency fo and bandwidth
2∆f can be realized from the un-terminated filter response in Fig. 1-10 by flattening the passband
with proper termination. (1-25) shows that ∆f, therefore the filter passband bandwidth after
termination, is controllable by stiffness of the coupling beam to that of the resonator at the
coupling location. In particular, for narrow-band filters, ∆f/fo is small, and (1-25) can be
simplified to
f 
1 
C
kca
 1    1  r 
fo 
2 
2Cca 2 c 1 c 2 kr
(1-26)
The last equation is established by substituting Cr and Cca with the expressions in (1-11) and
(1-13), respectively.
1.2.5 Half-Wavelength Couplers for Composite-Array Resonators
For extensional mode coupling beams of length designed to be integer number of halfwavelength coupler, i.e., Lc/λn=N±0.5, N=1, 2,…, equations (1-5) and (1-6) yields to the relation
Z a  Z b  2 Z c
or
10
(1-27)
2C ca  2C cb  C cc
(1-28)
Plugging (1-27) and (1-28) to (1-19) and (1-20) yields

1
2 sC sa
i1
0.5
0.5
0.5




1
v1


1  


   
sC sa
sC sa 

(1-29)
1
2 sC sa
i2
0.5
 0.5
0.5




1
v1



1 


   
sC sa
sC sa 

(1-30)
The approximation holds true as the value of Csa approaches infinite as the length of the
coupling beam approaches half-wavelength. The resonant frequency of this resonator arraycomposite is the same as that of its constituent resonator, fo. Ideally, array-composite resonator
behaves as a single resonator, with impedance related to the drive and sense schemes.
If one resonator is excited and the in-phase output current is collected from the other
resonator, shown in Fig. 1-8(b), and assuming each electrode has identical dimension, the
magnitude of the output current is
i2
v1

C sa0
0.5
(1-31)

Compared to a single resonator in Fig. 1-8(a), this array-composite generates half of the
output currents and has twice the impedance.
Another case is when one resonator is excited and the in-phase output currents are collected
from both resonators. Again, assuming each electrode is identical in dimension, the magnitude of
the total output currents is
i1
v1

C sa 0
i2
v1

C sa 0
1
(1-32)

If both resonators are excited and both resonators are sensed, superposition of voltage
sources can be used to obtain
i1
v1

C sa 0 , v2  0
i2
v1

C sa 0 , , v 2  0
i1
v2

C sa 0 , v1  0
i2
v2

C sa 0 , , v1  0
2

(1-33)
The output current is twice than that of a single resonator. Chapter 5 will explore the effect
on electrode placement and mechanical coupling on the impedance of similar resonator array in
greater details.
11
The above circuit analysis can be applied to analyze systems with even higher degrees of
freedom by using matrixes of higher ranks.
1.2.6 Filter Termination
As discussed in Section 1.2.4, two identical resonators coupled by quarter-wavelength
coupling beams show two peaks on the frequency spectrum, corresponding to two mode shapes
of the two-degree freedom system. Fig. 1-9 shows the simulation results of such coupled
resonators, where the in-phase and out-of-phase mode shapes render resonant peaks at lower and
Rs
io
vi
Rs
VP
(a)
vo
Rs
vo
vi
Rs
VP
(b)
Rs
vo
vi
Rs
VP
(c)
Rs
vo
vi
(d)
Rs
VP
Fig. 1-8: (a) a single disk resonator with the input signal vi and output current io; (b)-(d) disk
array-composite resonator with different measurement setup: (b) drive one resonator and sense
the other; (c) drive one resonator and sense both resonators; (d) drive and sense both resonators
renders twice the output currents, thus half the impedance, compared to a single resonator in (a).
12
higher frequencies, respectively.
To flatten the filter passband in Fig. 1-10, the Q‘s of the end resonators must be loaded via
resistive termination with value of RQ given by [16]
 Q

Q mr  o mr B
RQ   r  1  Rx 


2
 qQ

qQ
Q

q e2
f
f
e


(1-34)
where Rx is the motional resistance of a constituent end resonator; Q is the unloaded quality
factor of the resonator; Qfltr = fo/B, B being the filter passband width; q is a normalized parameter
obtained from a filter cookbook [18]; mr is the dynamic mass of the resonator at its point of
maximum displacement; and ηe is the electromechanical coupling factor.
Fig. 1-10(a) shows a typical terminated micromechanical filter consisting of two identical
contour-mode disk resonators. The termination resistance RQ affects the input and output
impedances of the filter, which must be considered in the design of the neighboring circuits, such
as low-noise amplifier, to optimize the power transfer and noise figure. From the expression of
RQ in (1-34), manipulation of ηe is the most convenient way for achieving a specific value of RQ.
While it is an option to increase ηe by increasing the transducer and resonator sizes, the
interaction of RQ and the physical capacitance at the input and output ports dictates another
requirement on the resonator performance, as will be discussed in the next section.
1.2.7 Filter FOM
As shown in Fig. 1-10(a), the RQ and Co essentially combine to generate a pole at b =
1/(RQCo) that sets the 3 dB bandwidth of a low-pass filter, b. Co models the physical capacitance
0
S21 (dB)
Terminated
Filter Response
-20
-40
-60
0.95
Un-terminated
Filter Response
1.00
1.05
1.1
Frequency (GHz)
1.15
Fig. 1-9: Simulation results of terminated and un-terminated filter responses. The termination
resistors RQ‗s ‗flatten‘ the peaks corresponding to two mode shapes of the mechanically coupled
two-resonator composite.
13
associated with the input and output ports, including those of the transducers, interconnects, and
the neighboring circuits. Therefore, a terminated MEMS filter can be modeled by a bandpass
filter in series with two low pass filters, shown in Fig. 1-10(b). If b is lower than the center
frequency o of the filter, it will add undesired passband loss. When b is larger than o but
somewhat close to o, it may cause the phase lag significant enough to distort the passband [14].
1/(RQCo) can also be considered as the transducer bandwidth and it is not a function of resonator
Q. (1-34) suggests that mr and ηe are the only tunable parameters to optimize RQ given filter
bandwidth B and normalized parameter q for a specific application. Therefore, the filter figure of
merit aimed to evaluate a resonator (more precisely, a transducer) can be defined as,
FOM 
 e2
(1-35)
mr Co
(1-35) reveals that ηe2 /Co needs to be maximized for sufficient transducer bandwidth as well
as optimized ηe for impedance matching. The problem associated with the low-pass filters shown
in Fig. 1-10(b) is actually fixable by using an (on-chip) inductor to resonate out the Co, but it
would be preferable if an inductor were not needed. As will be derived in Chapter 4-1, the value
of 1/(RQCo)
The filter FOM in (1-35) is defined from the perspective of filter design. Another parameter,
kt , called the coupling efficiency, is more commonly used to evaluate the performance of
piezoelectric transducers and resonators. For resonators at the same frequency, the value of the
filter FOM is proportional to kt2 and both can be used to evaluate resonator performance
interchangeably. To see this, consider the electric model of a one port resonator, shown in Fig.
**, where the feedthrough capacitance Co is parallel to the series resonator tank. The impedance
of this circuit reaches the minimum and maximum at its series and parallel resonance
frequencies, respectively. The series resonance frequency is written as
2
io
RQ
vo
vi
Co
(a)
vi
Co
RQ
VP
Low-Pass
Filter
Channel-Select Band-pass Filter
Low-Pass
Filter
vo
(b)
Fig. 1-10: (a) A MEMS filter properly terminated with resistors RQ connected to both input and
output ports. The physical capacitance associated with the transducers and parasitic capacitance,
is modeled with Co. (b) RQ and Co form undesired low-pass filters which could affect the signal
integrity if their cut-off frequencies are lower than the passband of the band-pass filter.
14
Series Res. Tank
1/kr
mr
cr
Co
Fig. 1-11: Equivalent electrical model of a one-port resonator.
fs 
1
2
1
Lx C x
(1-36)
The parallel resonance frequency is written as
fp 
1
2
Cx
Co
1

Lx C x
2
1
1
Lx C x

C 
 1  x 
2C o 

(1-37)
The approximate was valid as long as Co is much larger than Cx, which is true for properly
designed MEMS resonators at the frequencies of interest.
kt2 is defined as
kt2 
 2 f p  fs

4
fp
(1-38)
Replacing fs and fp with the expressions in (1-36) and (1-37) gives
kt2 
 2 Cx

8 Co
(1-39)
Replacing Cx in (1-38) with the expression in (1-11) results
kt2 
2
2
 2  e2
2


 2 e
 e
8 kr C o
8  o mr C o mr C o
(1-40)
(1-40) states that given the same resonator design, the value of kt2 is proportional to that of the
FOM defined in (1-35) and both parameters can be interchangeable to evaluate the resonators.
15
1.2.8 Filter Insertion Loss
The insertion loss of the filter, as shown in Fig. 1-4, can be written as:
 Rx  RQ
IL  20 log
 R
Q




Qr

  20 log

Q q Q 
f 

 r
(1-41)
where Qr is the Q‘s of constituent resonators and Qf is the ratio of the filter center frequency to
the filter bandwidth. Qf is the reciprocal of the filter percent bandwidth. (1-41) shows
dependence of insertion loss on Q‘s of constituent resonators and the filter, where q is the same
normalized parameter used in (1-34), which value depends on the filter type, ripple requirement,
and filter order. As the insertion loss of an RF filter directly adds to the noise figure of the
preceding low-noise amplifier (LNA), it is important to minimize the filter insertion loss.
Fig. 1-12 illustrates the dependence of insertion loss on resonator Q via plots of frequency
response for 2-resonator filters with 1% (i.e., Qf = 1,00) and 0.1% (i.e., Qf = 1,000) bandwidths,
over various constituent resonator Q‘s. Here, to assure less than 3 dB insertion loss, the
minimum required resonator Q is only 1,000 for a 1%-bandwidth filter, but as high as 10,000 for
0.1%-bandwidth, clearly emphasizing the importance of Q when small percent bandwidths are
needed.
Fig. 1-13 shows simulation of the dependence of filter insertion loss on resonator Q using
q=1.6 for a two-pole Gaussian filter with different filter passband percent bandwidth. Most bandselect filters have small Qf, e.g., Qf = 36 for GSM (with receiving bandwidth of 25 MHz and
center frequency of 900 MHz) and Qf = 95.5 for UMPS (with receiving bandwidth of 20 MHz
(a)
-5
-10
0
Q=2,000
Insertion
Loss
Q=300
Q=1,000
(3 dB loss)
Q=400
-15
Q=200
-20
-25
Transmission (dB)
Transmission (dB)
0
1% BW
-30
-20
0
+10
-10
Freq. Offset from 1GHz (MHz)
+20
(b)
Q=20,000
-5
-10
Q=10,000
(3 dB loss)
Q=3,000
Q=4,000
-15
-20
Q=2,000
-25
0.1% BW
-30
-2
-1
0
+1
+2
Freq. Offset from 1GHz (MHz)
Fig. 1-12: Simulated frequency characteristics for 1-GHz filters with varying constituent
resonator Q‘s, illustrating how resonator Q governs the insertion loss of a filter. (a) For an
insertion loss less than 3 dB, resonator Q‘s must be larger than 1,000 for a 1 % bandwidth filter.
(b) When the filter bandwidth shrinks to 0.1 %, even higher resonator Q > 10,000 is needed.
16
Insertion Loss (dB)
Qf = 2,300
Qf = 1,200
Qf = 500
Qf = 100
Resonator Quality Factor Qr
Fig. 1-13: Simulated dependence of filter insertion loss on Qr for different Qf. To ensure less than
3 dB insertion loss, the required Qr increases as Qf increases (i.e., narrower bandwidth for the
same filter center frequency.)
and center frequency of 1910 MHz), and require only Qr > 523 to maintain the insertion loss to
be less than 3 dB. Channel-select filters, on the other hand, needed at the front-end of a cognitive
radio require small percent bandwidth filters that in turn demand very high Q resonators to avoid
excessive insertion loss. In particular, channel-select filters designed for 900MHz GSM will have
Qf = 2,250 (with filter bandwidth of 0.4 MHz) and demands Qr > 12,300 for insertion loss less
than 3 dB.
The requirement on resonator Q for low filter insertion loss further sets the requirement on
the resonator impedance Rx For the same filter percent bandwidth (i.e., same Qf) and resonator Q
(i.e., same Qr), achieving lower filter insertion loss requires larger RQ/Rx, and thus larger RQ and
transducer bandwidth. In particular, to ensure less than 3 dB filter insertion loss, the RQ/Rx ratio
needs to be larger than 2.4. Therefore, if the optimal design requires RQ = 1 kΩ, the resonator
needs to be designed with Rx = 417 Ω.
It should be noted that according to (1-41), filter insertion loss is only a function of filter
percent bandwidth and is independent of filter center frequency. However, it is generally more
difficult to achieve higher Q at higher frequencies as the resonators suffer from more phononphonon interaction loss and prone to anchor loss at higher frequencies.
In summary, narrow-band MEMS filters operating at GHz require high coupling to ensure
sufficient transducer bandwidth and high resonator Q to ensure low insertion loss. Unfortunately,
current MEMS resonators can meet only one requirement, but not both. The following two
sections review the previous work of the two most promising transduction methods for MEMS
resonators: capacitive and piezoelectric transduction.
17
1.3 Previous Work on Capacitive MEMS Resonators
Capacitive, or electrostatic, resonators enjoy a wide range of resonant structure materials, as
any conductive material, or insulators coated by conductive thin films, can form parallel plate
capacitors for electrostatic transduction. This section outlines the common materials used for
capacitive resonators in the literature.
1.3.1 Single-Crystal Silicon Capacitive Resonators
The two main advantages of using single-crystal silicon as the resonator structure are larger
vertical dimension for larger transducer forces and consistent material properties. Resonators as
thick as 20 µm [19] have been successfully fabricated on SOI wafer using DRIE to pattern the
resonator structure and HF etch of box oxide to release the structure. The single-crystal property
allows resonator dimension to scale down to 10 nm [20] with predictable material properties. On
the other hand, single-crystal silicon is anisotropic such that its Young‘s modulus is different
along different crystalline planes, which could possibly cause problems to movable mechanical
structures with certain geometries.
1.3.2 Poly-Si and Poly-SiGe Capacitive Resonators
Unlike single crystal silicon wafer substrate, poly-Si and poly-SiGe thin-films deposited via
low-temperature chemical vapor deposition (LPCVD) do not have homogeneous material
properties on the nano-meter scale due to various grain sizes and grain boundaries. However,
they are sometimes the preferred materials to use for better defined support beam lengths and
anchoring positions, exemplified by a disk resonator with self-aligned anchor in Fig. 1-14 [21].
In particular, low-temperature deposition of SiGe with SiH4 and GeH4 allow the MEMS
resonators to be built directly on CMOS for the MEMS-last integration scheme [22].
1.3.3 Metal Capacitive Resonators
Even lower process temperature for CMOS integration, cheaper process, smaller parasitic
resistance drive the efforts for developing metal capacitive resonators, either using the back-end
metal stacks of CMOS or metal thin-films deposited on CMOS back-end. Implementing MEMS
resonators using the CMOS back-end metal and inter-layer dielectric (ILD) stacks [6][23]
provided by foundry services has the advantage of well-controlled material property but with
limitations on film thickness and difficulty of realizing small lateral transducer gap spacing. An
example of CMOS-MEMS resonator is shown in Fig. 1-15(a). Among metal capacitive
resonators in the published literature, both the highest frequency and quality factor Q have been
achieved with electroplated nickel, shown in Fig. 1-15(b), demonstrating Q=54,507 at 59.96
MHz for a stemless disk resonator [24] and Q=2,467 at 425.7 MHz for a ring resonator [25].
There is strong evidence that anchor loss dominates the Q for resonators measured in vacuum.
Reduction of anchor loss via optimized design of support beams and anchoring points has been
shown to successfully enhance the Q by as much as 28 times for beam resonators [26] and 2.5
times for ring resonators [27], respectively. Such optimal anchors are difficult to achieve from
back-end metal stacks with stringent design and layout rules.
18
(a)
(b)
(c)
Fig. 1-14: (a) a bar resonator made of 20 µm thick single-crystal silicon [19]; (b) a poly-silicon
disk resonator with self-aligned stem [21]; (c) a P+ poly-Si0.35Ge0.65 resonator fabricated on top of
a CMOS amplifier [22].
(a)
(b)
(c)
Fig. 1-15: (a) a CMOS-MEMS beam resonator made of backend ILD and metal of a CMOS chip
[6]; (b) a ring resonator made of electroplated nickel [25]; (c) a poly-diamond disk resonator
[28].
1.3.4 Other Materials
Some exotic materials (exotic compared to silicon and metal) arise as the promising materials
for extremely high performance MEMS resonators due to their theoretically higher f·Q products
than silicon and metal. In particular, diamond disk resonators (Q = 55,300 at fo= 497.6 MHz),
shown in Fig. 1-15(c) achieved 13.86x higher f·Q product than poly-silicon ones (Q = 8,100 at
fo= 245.1 MHz) with the same geometry (contour-mode disk with diameter of 22 µm) and
anchoring method (center stem with diameter of 1.6 µm) [28].
19
1.4 Previous Work on Piezoelectric MEMS Resonators
As will be discussed in more detail in Chapter 4.1, piezoelectric transduction offers order of
magnitudes higher coupling coefficient than capacitive ones for similar resonator geometry.
Although the Q‘s of thin-film piezoelectric resonators have been measured to be historically
lower than those of capacitive counterparts, the low impedance enabled by the much higher
coupling of piezoelectric transduction makes piezoelectric resonators the preferred technology in
some applications. Unlike capacitive transduction in which any conductive material can be used,
piezoelectric transduction relies on the piezoelectricity that only exists in some materials, i.e.,
piezoelectric materials. Common materials for MEMS piezoelectric resonators are thin quartz
plates, sputtered ZnO, and sputtered AlN.
1.4.1 SAW Resonators
Surface Acoustic Wave (SAW) resonators normally use inter-digital transducer (IDT)
electrodes to convert electric energy to mechanical energy in the form of Rayleigh waves, which
have a longitudinal and a vertical shear component and propagate along the surface of bulk
piezoelectric substrates [29], a schematic of which is shown in Fig. 1-16(a) [29]. While the IDT
electrodes can be patterned using standard lithography, the need for bulk piezoelectric substrates
impedes the single chip integration with today‘s silicon-based CMOS chips.
1.4.2 FBAR and BAW Resonators
A film piezoelectric thickness-extensional bulk mode resonator consists of a piezoelectric
material film, normally on the order of several micrometers to tenth of micrometers, sandwiched
between electrodes [31]. Such devices are called film bulk acoustic resonators (FBAR) or bulk
acoustic wave (BAW) resonators depending on the thickness of the piezoelectric film. To
achieve higher Q, the resonant structure is acoustically isolated from the surrounding medium via
air gaps [32] or Bragg acoustic deflectors [33] composed of stacked layers of materials with
mismatched acoustic impedances (Fig. 1-16(c); the latter has better power handling capability.
Common piezoelectric thin-film materials include AlN, ZnO, and PZT, among which PZT gives
the highest piezoelectric coupling coefficients (~60x higher than AlN), which is good, but also
undesirably high permittivity (~100x higher than AlN), which is usually not suitable for high
frequency applications. Sputtered AlN offers decent coupling and permittivity and is easier to
process at room temperature, therefore has proven commercially viable for RF applications [34].
1.4.3 Lateral-Mode Thin-Film AlN Resonators
Despite the current market dominance of FBAR in the RF filter market for wireless handsets, the
dependence of resonant frequency on the AlN film thickness preclude realization of multiplefrequency resonators with one AlN deposition step. Piazza et. al. pioneered the research in
lateral-mode thin-film AlN resonators [35], shown in Fig. 1-16(c), as a technically feasible way
to expand the major advantage of FBAR devices have over capacitive ones, namely, low
motional impedance, to single chip implementation of multiple frequencies. This is possible as
20
(a)
(b)
(c)
Fig. 1-16: (a) schematic of a typical SAW resonator [29] where metal layers are patterned to be
inter-digital transducers on bulk piezoelectric materials, such as quartz crystal and LiTaO3. (b)
SEM cross-sectional image of[33] (c) SEM image of a contour-mode AlN ring resonator which
achieve motional impedance of 56 Ω [35]a contour-mode AlN ring resonator which achieve
motional impedance of 56 Ω [35].
for lateral mode devices, resonant frequency is determined by the lateral dimensions defined by
lithography, rather than AlN film thickness. However, for the current lateral mode resonators
made of sputtered AlN thin films, quality factors remain less than 3,500. Q‘s less than 10,000
render insertion loss of channel-select filters larger than 3 dB, as shown in Fig. 1-16. This
prevents the current AlN resonators to be applied to channel-select filters, despite its advantage
on easier filter termination.
1.5 Thesis Outline
This thesis is organized as follows:
In Chapter 2, simulation shows insufficient coupling efficiency of current electrostatic
transducers to be used in GHz channel-select filters. Close examination on the equation
governing the force transduction and transducer efficiency reveals that reduction of transduction
gap spacing is the most effective way among others to enhance coupling efficiency. To address
the difficulty in release sub-50nm gap spacing, a new technique in which partial filling of the gap
with high-k dielectric deposited via atomic layer deposition (ALD) reduces the gap spacing from
97nm down to effectively 32nm.
Chapter 3 first reviews the inherent limitations on release high-aspect ratio MEMS structures
using either dry or wet etch. Realizing that the limitation exists regardless the chemicals involved
in the etching, as long as one or more sacrificial materials need to be removed, a etch-free release
method is purposed and demonstrated, in which the volume reduction property of silicidation is,
for the first time, being used to generate gaps and to release MEMS structures using only
seconds of silicidation annealing.
21
Another direction to achieve simultaneously low-impedance and high Q resonators is to raise
the Q of piezoelectric resonators without raising their impedance. Chapter 4 proposes and
demonstrates a method for raising Q by eliminating losses associated with contacting electrodes.
Chapter 5 further provides an alternative solution for raising the Q of piezoelectric resonators
by energy sharing among resonators with and without electrodes. This method can further be
used to combine the advantages of high coupling from piezoelectric transducers and low loss
property from extremely high Q materials.
Chapter 6 concludes the above research and provides a view on the future research.
1.6 References
[1] C. T.-C. Nguyen, "Integrated micromechanical RF circuits for software-defined cognitive
radio," 26th Sym. on Sensors, Micromachines, and App. Sys., 2009, pp. 1-5.
[2] G. Piazza, P. J. Stephanou, and A. P. Pisano, "Piezoelectric Aluminum Nitride Vibrating
Contour-Mode MEMS Resonators," J. Microelectromech. Syst., vol. 15, no. 6, pp. 14061418, 2006.
[3] E. A. Gerber and M. H. Miles, "Reduction of the frequency-temperature shift of
piezoelectric resonators by mechanical stress," Proceedings of the IRE, vol. 49, pp. 16501654, 1961.
[4] J. Berge, M. Norling, A. Vorobiev, and S. Gevorgian, "Field and temperature dependent
parameters of the dc field induced resonances in BaxSr1-xTiO3- based tunable thin film bulk
acoustic resonators," Journal of Applied Physics, vol. 103, pp. 064508-064508-8, 2008.
[5] C. Qingming, Z. Tao, and W. Qing-Ming, "Frequency-temperature compensation of
piezoelectric resonators by electric DC bias field," Ultrasonics, Ferroelectrics and Frequency
Control, IEEE Transactions on, vol. 52, pp. 1627-1631, 2005.
[6] W.-C. Chen, W. Fang, and S.-S. Li, "Quasi-linear frequency tuning for CMOS-MEMS
resonators," Proceedings, 24th Int. IEEE Micro Electro Mechanical Systems Conf., pp. 784787, 2011.
[7] L. Hurley, "A temperature-controlled crystal oscillator," in Frequency Control, 1989.,
Proceedings of the 43rd Annual Symposium on, 1989, pp. 55-57.
[8] A. S. Margulies and J. Mitola, III, "Software defined radios: a technical challenge and a
migration strategy," Proceedings, Spread Spectrum Techniques and Applications, IEEE 5th
International Symposium on, 1998, pp. 551-556 vol.2.
[9] L. Canxing, H. Lu, and L. Wenjia, "A 2-Bit 4GS/s flash A/D converter in 0.18 µm CMOS
for an IR-UWB communication system," in Solid-State and Integrated-Circuit Technology,
2008. ICSICT 2008. 9th International Conference on, 2008, pp. 1965-1968.
[10] B. Verbruggen, P. Wambacq, M. Kuijk, and G. Van der Plas, "A 7.6 mW 1.75 GS/s 5 bit
flash A/D converter in 90 nm digital CMOS," in VLSI Circuits, 2008 IEEE Symposium on,
2008, pp. 14-15.
22
[11] M. Choi, L. Jungeun, L. Jungho, and S. Hongrak, "A 6-bit 5-GSample/s Nyquist A/D
converter in 65nm CMOS," in VLSI Circuits, 2008 IEEE Symposium on, 2008, pp. 16-17.
[12] R. Bagheri, A. Mirzaei, S. Chehrazi, M. Heidari, M. Lee, M. Mikhemar, W. Tang, A. Abidi,
―An 800MHz to 5GHz software-defined radio receiver in 90nm CMOS,‖ Dig. of Tech.
Papers, Int. Conf. on Solid-State Circuits (ISSCC), 2006, pp. 1932-1941.
[13] Z. Ru, E. A. M. Klumperink, G. J. M. Wienk, B. Nauta, ―A software-defined radio receiver
architecture robust to out-of-band interference,‖ Dig. of Tech. Papers, Int. Conf. on SolidState Circuits (ISSCC), 2009, pp. 230-231.
[14] K. Wang, A.-C. Wong, and C. T.-C. Nguyen, ―VHF free–free beam high-Q
micromechanical resonators,‖ J. Microelectromech. Syst., vol. 9, no. 3, pp. 347–360, 2000.
[15] R. A. Johnson, Mechanical Filters in Electronics. New York: Wiley, 1983.
[16] F. D. Bannon, J. R. Clark, and C. T.-C. Nguyen, ―High-Q HF microelectromechanical
filters,‖ J. Solid-State Circuits, vol. 35, no. 4, pp. 512–526, 2000.
[17] S.-S. Li, Y.-W. Lin, Y. Xie, Z. Ren, and C. T.-C. Nguyen, ―Small percent bandwidth design
of a 431-MHz notch-coupled micromechanical hollow-disk ring mixer-filter,‖ Proceedings,
IEEE Int. Ultrasonics Symposium, Sept. 18-21, 2005, 1295-1298.
[18] A. I. Zverev, Handbook of Filter Synthesis. NY: Wiley, 1967.
[19] S. Pourkamali, G. K. Ho, and F. Ayazi, "Low-Impedance VHF and UHF Capacitive Silicon
Bulk Acoustic Wave Resonators Part I: Concept and Fabrication," in Transactions, IEEE
Electron Devices, vol. 54, pp. 2017-2023, 2007.
[20] D. Weinstein1 and S. A. Bhave, ―Acoustic resonance in an independent-gate FinFET,‖ Tech.
Digest, Solid-State Sensor, Actuator, and Microsystems Workshop, Hilton Head, South
Carolina, 2010, pp. 459-462.
[21] J. Wang, Z. Ren, and C. T.-C. Nguyen, ―Self-aligned 1.14-GHz vibrating radial-mode disk
resonators,‖ Dig. of Tech. Papers, Int. Conf. on Solid-State Sensors & Actuators
(Transducers‘03), Boston, Massachussets, June 8-12, 2003, pp. 947-950.
[22] A. E. Franke, J. M. Heck, T.-J. King, and R. T. Howe, ―Polycrystalline silicon—Germanium
films for integrated microsystems,‖ J. Microelectromech. Syst., vol. 12, no. 2, pp. 160–171,
2003.
[23] C-C Lo, F. Chen, and G. K. Fedder, ―lntegrated HF CMOS-MEMS square-frame resonators
with on-chip electronics and electrothermal narrow gap mechanism,‖ in Tech. Dig.,
Transducers’05, 2005, pp. 2074–2077.
[24] W.-L. Huang, Z. Ren, and C. T.-C. Nguyen, "Nickel vibrating micromechanical disk
resonator with solid dielectric capacitive-transducer gap," in Proc. IEEE Int. Freq. Control
Symp. pp. 839-842, 2006.
[25] W.-L. Huang, S.-S. Li, Z. Ren, and C. T.-C. Nguyen, ―UHF nickel micromechanical spokesupported ring resonators,‖ Dig. of Tech. Papers, Int. Conf. on Solid-State Sensors &
Actuators (Transducers‘07), 2007, pp. 323–326.
[26] K. Wang, A.-C. Wong, C. T.-C. Nguyen, ―VHF Free–Free Beam High-Q Micromechanical
Resonators,‖ J. Microelectromech. Syst., vol. 9, no. 3, pp. 346–360, 2000.
23
[27] S.-S. Li, Y.-W. Lin, Y. Xie, Z. Ren, and C. T.-C. Nguyen, "Micromechanical "hollow-disk"
ring resonators," in Tech. Digest., 17th IEEE Int. MEMS Conf., pp. 821-824, 2004.
[28] J. Wang, J. E. Butler, T. Feygelson, and C. T.-C. Nguyen, ―1.51-GHz nanocrystalline
diamond micromechanical disk resonator with material-mismatched isolating support,‖
Proceedings, 17th Int. IEEE Micro Electro Mechanical Systems Conf., Maastricht, The
Netherlands, Jan. 25-29, 2004, pp. 641-644.
[29] P. S. Cross, "Reflective arrays for SAW resonators," in Ultrasonics Symposium, 1975, pp.
241-244.
[30] H. Kando, M. Watanabe, S. Kido, T. Iwamoto, K. Ito, N. Hayakawa, K. Araki, I. Hatsuda,
T. Takano, Y. Nagao, T. Nakao, T. Toi, and Y. Yoshii, "Improvement in temperature
characteristics of plate wave resonator using rotated Y-cut LiTaO3 structure," 24th Int. IEEE
Micro Electro Mechanical Systems Conf., 2011, pp. 768-771.
[31] M. Berte, "Acoustic bulk wave resonators and filters operating in the fundamental mode at
frequencies greater than 100 MHz," in 31st Annual Symposium on Frequency Control. 1977,
1977, pp. 122-125.
[32] M. Hara, J. Kuypers, T. Abe, and M. Esashi, "Aluminum nitride based thin film bulk
acoustic resonator using germanium sacrificial layer etching," Dig. of Tech. Papers, Int.
Conf. on Solid-State Sensors & Actuators (Transducers‘03), 2003, pp. 1780-1783.
[33] L. Mai, V.-S. Pham, and G. Yoon, ―ZnO-based film bulk acoustic resonator devices on a
specially designed Bragg reflector,‖ J. Applied Physics, vol. 95, pp. 667-671, 2009.
[34] R. Ruby and P. Merchant, ―Micromachined thin film bulk acoustic resonators‖, Freq.
Control Symp., pp.135-138, 1994.
[35] G. Piazza, P. J. Stephanou, J. M. Porter, M. B. J. Wijesundara, and A. P. Pisano, "Low
motional resistance ring-shaped contour-mode aluminum nitride piezoelectric
micromechanical resonators for UHF applications," 18th Int. IEEE Micro Electro Mechanical
Systems Conf., 2005, pp. 20-23.
24
Chapter 2: ALD Partially-Filled Gaps
2.1 Introduction
To date, capacitively transduced micromechanical resonators have posted the highest Q‘s of
room temperature on-chip resonator technologies, with Q values exceeding 150,000 in the VHF
range [1], 14,600 in the GHz range [2], and 560 up to 37 GHz [3]. This makes them strong
candidates for use as RF channel-selectors in next generation software-defined cognitive radios
[4], or as ultra-low noise oscillators in high performance radar applications and space
exploration.
Unfortunately, the exceptional Q‘s of these resonators are not easy to access, because the
impedances they present are often much larger than that of the system that uses them. For
example, many of today‘s board-level systems are designed around 50 impedance, which is
much smaller than the 2.8 k termination resistors required by the 163 MHz differential disk
array filter of [5]. Thus, even though the filter of [5] attains an impressively low insertion loss of
2.43 dB for a 0.06% bandwidth, it requires an L-network to match to 50. While it is true that as
micromechanical filters are integrated together with transistors on single silicon-chips impedance
requirements will grow to the k range for best performance [6], off-chip board-level
applications will still need lower impedance.
Pursuant to attaining lower capacitive micromechanical resonator impedances, this work,
first published in [7], employs atomic layer deposition (ALD) [8] to partially fill the electrode-toresonator gaps of released disk resonators with high-k dielectric material and thereby achieve
substantially smaller gap spacing, as small as 32 nm. This reduction in gap spacing increases the
electromechanical coupling factors (e‘s) of capacitive-transducers by a factor of 8.1×; this not
only lowers termination impedances for capacitively transduced micromechanical filters from
the k range to the sub-100-range, thereby making them compatible with board-level RF
circuits, but does so in a way that reduces micromechanical filter termination resistance RQ much
faster than the electrode-to-resonator overlap capacitance Co. Thus, gap reduction substantially
increases the 1/(RQCo) figure of merit (FOM). The increase in the FOM is also n2× faster (hence,
better) than that of fully-filled solid-dielectric gap methods for Rx reduction [9]. This partial
dielectric-filling based approach further prevents shorting of the resonator to its electrode, which
greatly improves the resilience of micromechanical resonators against ESD or other events that
might pull a resonator into its electrode.
2.2 Coupling Efficiency of Capacitive Transducers
2.2.1 Capacitive Transducers
Fig. 2-1(a) shows a parallel plate capacitor system in which one plate is fixed and the other
plate is attached to a spring, forming a spring-mass-damper system, which is essentially a
resonator. With the input signal vi and DC bias VP applied to the system, the electrostatic force
25
C(t)
io
cr
d2
mr
d1
VP + vi
(a)
io
VP
kr
(b)
io
Resonator-Electrode
Overlap Area = A2
Resonator-Electrode
Overlap Area = A1
(c)
fo
f
Fig. 2-1: (a) Schematic of a capacitive transducer. (b) A simplified circuit model of (a) upon
resonance, where the VP biased time varying capacitor generate output current. (c) The output
current has energy concentrated at the resonant frequency of the resonator, showing a resonant
peak on the frequency domain.
generated between the resonator and the electrode plates can be written as
F  (VP  vi ) 2
C
x
(2-1)
where VP is a DC bias applied to the conductive resonator structure; C/x is the change in
electrode-to-resonator overlap capacitance per displacement. Assuming the time-varying
displacement x is much larger than gap spacing d, such that the nonlinearity can be ignored for
now, the force component in (2-1) that has a frequency component the same as vi is
F  VP v i 
o
A r  o
d2
(2-2)
where A is the electrode-to-resonator overlap area; εr is the relative permittivity of the electrodeto-resonator gap material (=1, if not present); εo is the permittivity in vacuum; and d is the
electrode-to-resonator gap spacing. The electromechanical coupling coefficient on the input side
models how efficiently the input electrical signal can be transduced to mechanical energy in the
form of mechanical force. It can therefore be written as the magnitude of mechanical force
generated per unit magnitude of input voltage:
 e ,i 
F
o
vi
 VP 
A1 r o
d12
(2-3)
Upon resonance, the vibration amplitude, x, modulates the gap spacing and therefore the
capacitance. With constant DC bias applied across the parallel plate, the stored charge changes
26
accordingly, resulting in output current when the output electrode is connected to a resistor. The
difference in stored charge, ∆Q, when the gap spacing changes from d to (d-x) is:
 1
1
A 
Q  VP  A2 r o  
   VP  2 2r o  x
d2
 d2  x d2 
(2-4)
The electromechanical coupling coefficient on the output side, ηo, models how efficiently the
mechanical energy stored in the resonator can be transduced to electrical energy as output
currents. It can be written as the amount of charge generated per mechanical displacement:
 e ,o 
Q
A 
 VP  2 2r o
x
d2
(2-5)
To simplify the following analysis, the parameters of both transducers on input and output
ports will be assumed to be the same, which results in equal electromechanical coupling
coefficients, denoted as ηe:
 e   e ,i   e ,o  VP 
Ao r  o
do2
(2-6)
2.2.2 Filter FOM of Capacitive Resonators
Consider a capacitive disk resonator with radius of R and thickness of H. The filter figure of
merit (FOM) defined in Chapter 1 for capacitive resonators can be related to parameters of
constituent resonators by plugging the coupling coefficients ηe in (2-6) into (1-33):
1
q e2
do
q 1  o VP2 r
FOM 




RQ Co Bmr Ao o r
B  R d 3
(2-7)
Where B is the filter passband width; q is a normalized parameter obtained from a filter
cookbook [10]; mr is the dynamic mass of the resonator at its point of maximum displacement; 
is a modifier that accounts for the integration needed to obtain dynamic stiffness [11]; is the
density of the disk structural material; and (2-7) was reduced to its final form by recognizing that
the dynamic mass of the disk at a maximum velocity point on the disk is mr = R2H.
Of the variables in (2-7), only r, VP, and d are truly adjustable, although the motional
impedance Rx can often be minimized by operating at a fundamental mode, rather than higher
modes. This implies that arraying approaches [12] or parallel combinations of multiple
resonators, shown in Fig. 2-2, reduces Rx and essentially increase the electrode-to-resonator
overlap area do not in fact raise the FOM. As the impedance reduces linearly to the number of
resonators involved, the capacitance also increases by the same rate. An approach similar to
parallel combinations for reducing the impedance is to increase the electrode-to-resonator
overlap area by increasing the lateral dimension of the resonator. This approach is applicable to
certain mode-shapes, such as the contour-mode ring in [2], where the resonant frequency is
determined by the width of the ring and independent of the average radius, as long as the latter is
27
io
vo
VP
RL
vi
Fig. 2-2: Connecting resonators in parallel reduces Rx linearly, but filter FOM remains the same.
Table 2-1: Comparison of approaches for RQ reduction and filter FOM improvement
Approach
e
RQ
Co
FOM
Arraying with n resonators
nx
n-1 x
nx
1x
Solid-gap filling with εr=n
nx
n-2 x
nx
nx
Increasing DC bias VP by n x
nx
n-2 x
1x
n2 x
Air gap reduction from do to d=do/n
n2 x
n-4 x
nx
n3 x
much larger than the former. This approach, however, also gives only smaller impedance but the
same filter FOM. On the other hand, solid-gap filling methods, such as in [9] and Fig. 2-3(a), that
raise r and reduce gap spacing at the same time, do improve the FOM, although the
improvement ends up being much less than the factor by which r increases, since the need to
compress the gap material often greatly reduces the benefits. In particular, the resonators
measured in [9] with 80 nm air gaps and 20 nm nitride solid gaps, with other parameters being
the same, show Q=52,400, Rx=12.36 kΩ and Q=25,300, Rx=1.51 kΩ, respectively, based on
which the improvement in the coupling coefficient is calculated to be 4x. This value is far from
the expected improvement factor of 112x gained from 4x reduction in gap spacing and 7x
increase from r of silicon nitride compared to air (or vacuum) as the gap material. Finally,
although FOM increases with the square of Vp, its value is often limited by the level of the DC
power supply, especially for the cases for on-chip integration, unless charge pumps can be used
to increase the available VP. Thus, it seems to still be gap spacing reduction that provides the
largest gain in FOM, with very strong third power dependence. In particular, a reduction in gap
spacing by 5× yields a 125× increase in FOM. Table 2-1 summarizes the efficacy of different
approaches to reducing RQ and increasing FOM.
Linearity issues will need to be curtailed, as the IIP3 of the disk will reduce as the gaps
shrink [14], but the effects are less consequential as frequencies rise (e.g., at GHz) and can be
alleviated in certain mechanical circuit networks.
28
2.3 Gap Reduction via Partial Gap Filling
2.3.1 Methods for Achieving Small Gaps
Evidently, from an FOM perspective, reducing the electrode-to-resonator gap spacing is the
best way to reduce RQ. Achieving smaller gaps, however, might not be so straightforward. This is
especially true for small lateral gaps, which is essential for lateral mode capacitive resonators.
The work in [15], with SEM shown in Fig. 2-3(b), demonstrated ~100 nm gap spacing by direct
dry etching a blanket Ge film to form a Ge blade, which is removed via wet etch to form an air
gap. In this case, the resolution in lithography and dry etch determines the minimum achievable
gap spacing. While photoresist lines as small as ~100 nm and ~10 nm can be patterned by deep
UV source and electron beam source, respectively, the real challenge lies in transferring such
small patterns to 1 µm or thicker films, resulting in high aspect ratio structures, via anisotropic
etching.
A more scalable method is to use sacrificial material deposition. For example, the process of
[16] achieves its sub-100nm lateral gaps using a sacrificial oxide sidewall film that is
sandwiched between the resonator and electrode during intermediate process steps, but then
removed via a liquid hydrofluoric acid release etchant at the end of the process to achieve the
small gap. Fig. 2-4 shows the last step of the fabrication process. Here, sacrificial sidewall layers
are removed via wet etching to release structures that will eventually move. This approach to
achieving lateral gaps, while effective for gap spacings above 50 nm, proves difficult for smaller
gap spacings with acceptable yield. In particular, smaller gap spacings make it more difficult for
etchants to diffuse into the gap toward the etch front and for etch by-products to diffuse away
from the etch front. While there is some evidence that a gaseous etchant capable of more easily
accessing and escaping the gap, such as vapor phase HF, might prove effective for releasing
structures with 10 nm gaps or less [17][18], with SEM of [18] shown in Fig. 2-3(c), gaps so
small (once released) might be overly susceptible to inadvertent shorting, due to ESD or other
catastrophic events.
(a)
(b)
(c)
Fig. 2-3: Methods for resolving small lateral transduction gaps for capacitive resonators. (a)
Solid gap formed by 20 nm thick nitride does not require release step for small gaps [9]. (b) A
~100 nm gap for SiGe resonators is formed by dry etching a Ge blade followed by SiGe
deposition and finally H2O2 etching to remove the sacrificial Ge [15]. (c) 10 nm air gaps, where
the arrows point to, are released by the vapor HF [18].
29
2.3.2 ALD Partial-Filling for Sub-50nm Gap Spacing
Rather than removing material from small gaps by etching as drawn in Fig. 2-4, one
alternative approach to attaining both sub-50nm high-aspect-ratio gaps and protection against
ESD events is to partially fill an already released gap with a non-conductive dielectric material,
as shown in Fig. 2-5(a). Here, filling via a dielectric is just as effective as if filling were
performed with a metal if the permittivity of the dielectric is high enough to allow the air (or
vacuum) gap of Fig. 2-5(b) to set the overall capacitance value. Specifically, the capacitance
between the electrode and resonator of Fig. 2-5(a) can be modeled by the series connection of
three capacitors shown in Fig. 2-5(b). Here, the total electrode-to-resonator capacitance is given
by
C ( x)  Ccoat || Cair ( x) || Ccoat 
Ccoat
|| Cair ( x)
2
(2-8)
where both Ccoat have identical values as the same thickness of dielectric is deposited on all of
the surfaces. From (2-8), (C/x) can be written (for small x) as
Sacrificial
oxide
Poly Disk
Transduction
Gap
HF Release
Etching
Poly Disk
Fig. 2-4: Cross-sections depicting the final release step in the fabrication sequence for a
laterally driven wine-glass disk resonator.
Resonator Structure
Electrode
C
Substrate
Ccoat Cair Ccoat
c
dcoat
dair
Fig. 2-5: (a) Schematic of a partial-dielectric-filled gap. (b) Enlarged view of the gap and its
equivalent series capacitances.
30
2
C
1  Ccoat
1

 Ccoat


|| Cair  
|| Cair 


x  o Ao  2
d airCair  2


2
(2-9)
where Cair is the capacitance across the air gap for x = 0 (i.e., no displacement); Cair(x) is this
capacitance as a function of displacement x; Ccoat is the capacitance across each dielectric-coated
region; Ao is the resonator-electrode overlapping area. Naturally, if Ccoat >> Cair, then the
capacitance and (C/x) reduce to
C ( x)  Cair ( x)
(2-10)
C Cair

x d air
(2-11)
Therefore,
which are the values that would ensue if there were no dielectric and if the electrode-to-resonator
gap were equal to dair. In practice, Ccoat/2 should be at least 10 times larger than Cair in order for
(2-11) to be valid, which means that the dielectric constant of the filling material should be at
least
 coat  20 o
dcoat
d air
(2-12)
where the gap dimensions dcoat and dair are indicated in Fig. 2-5. For the case where the gap
spacing of a disk resonator is reduced from 94 nm to 32 nm with high-k dielectric coating,
achieving a (dcoat/dair) ratio of (31/32) and providing a 74x reduction in RQ, (2-12) suggests that
the relative permittivity of the dielectric filling material should be >19.4 to allow the use of (211) to determine (C/x); otherwise (2-9) should be used. Hafnium oxide (HfO2) comes close
and so is a reasonable choice of dielectric.
As the impedance is sensitive to the final gap spacing, the deposition of high-k dielectric
films must provide precise thickness control. Furthermore, to attain high-aspect-ratio sub-50nm
gaps, the starting gap size should already be small (e.g., on the order of 100 nm), so the method
used to fill the gaps should be very conformal. Recognizing this, atomic layer deposition (ALD)
is uniquely suited for this gap-coating process, since its two-step precursor, monolayer-bymonolayer deposition methodology effects very precise film thicknesses with conformality
sufficient to uniformly cover the surfaces of the 30:1 aspect ratio (100 nm initial gaps of the 3
µm thick resonators).
2.3.3 Atomic Layer Deposition (ALD)
Indeed, thin high-k dielectric films, such as hafnium and zirconium oxide films, have been
prepared by a variety of physical vapor deposition (PVD) methods, such as laser pulse ablation
[19] and sputtering [20], and chemical vapor deposition (CVD) with various precursors [21].
PVD methods provide excellent film composition and thickness control, but they do not deposit
conformally over high-aspect-ratio structures and so are not suitable to partially refill lateral
31
Steps (a) to (d) Forms One Cycle
Excess Tetratis
Hafnium
Reaction
Product
Hf
Hf
Hf
Hf
Hf
H
Hf
Hf
Hf
Hf
Hf
H
Hf
Hf
Hf
Hf
Hf
Hf
Substrate
(a) Precursor Expose
(b) Purge
Excess
Water
Reaction
Product
f
f
Hf
Substrate
Substrate
Substrate Treatment
Hf
H
Hf
Hf
H
f
f
Hf
Hf
H
H
Hf
f
f
Hf
Substrate
Substrate
Substrate
After Four Cycles
(d) Purge
(c) Water Vapor Expose
Fig. 2-6: HfO2 as an example to illustrate the steps of ALD of high-k dielectrics, where repeated
exposure and purge cycles of metal and oxygen precursors are performed.
gaps; CVD method typically requires deposition temperature higher than 300°C, which causes
formation of crystalline films with detectable surface roughness.
Atomic layer deposition (ALD) offers conformal high-k dielectric thin films by alternately
exposing the surface to reactive metal and oxygen precursors. Water vapors or ozone are
common choices of oxygen precursors. A purge step follows each precursor exposure step. Such
exposure-purge combination results in successive surface reaction between the precursor
introduced and the other precursor already adsorbed to the surface in the previous exposure step.
Each cycle deposits only an atomic layer of the target metal dielectric. The ALD process of HfO2
is summarized in Fig. 2-6. Among a variety of possible precursors, this work uses tetrakis
(ethylmethylamido) hafnium and water vapor [23].
32
io
A’
Anchor
B
B’
Wine Glass
Disk Resonator
vo
RL
vi
Electrodes A and
A’ are connected
A
(a)
Input
Electrode
VP
Output Electrode
d
Quasi-nodal
Points
Electrode
C
(b)
Electrodes B and
B’ are connected
Original
Edge
(c)
Substrate
Fig. 2-7: (a) Schematic of measurement setup for a wine-glass disk resonator. (b) Equivalent
mechanical mass-spring-damper system of (a). (c) The mode shape of wine-glass mode
vibration, where the disk expands and contracts along orthogonal axes.
2.4 Experimental Results
2.4.1 Wine-Glass Disk Resonator
Fig. 2-7(a) shows a wine-glass disk resonator with the measurement setup where AC signal is
applied to one set of the electrodes (B-B‘) and the output current is sensed from the other set (AA‘); DC bias is applied to the conductive resonator structure. The disk is suspended above the
substrate and supported by beams attached to the disk at two of the four quasi-nodal points of the
wine-glass mode shape, shown in
Fig. 2-7(c), where the disk expands and contracts along orthogonal axis. When the frequency
of input AC signal matches the wine-glass mode resonance frequency, the disk starts to vibrate.
The resonant frequency fo is given by [24]
33
 
 n 
 


2
  2  q  n    2  q  4q  1


(2-13)
where
n  x  
xJ n1 ( x )
J n ( x) ,
q
2
6
,
  2fo R
 ( 2  2 )
,
E

2
1
(2-14)
where Jn(x) is Bessel function of first kind of order n; R is the disk radius; ρ, σ, and E, are the
density, Poisson ratio, and Young's modulus, respectively, of the disk structural material, in this
case, poly-silicon. The resonance frequency of the wine-glass mode is, to the first order,
inversely proportional to disk radius R. The complete equations for calculating the equivalent
mass, stiffness, and coupling coefficients can be found in [25], which will not be repeated here.
These wine-glass disk resonators were fabricated with a three-polysilicon process described
in [26] and released in hydrofluoric acid (HF). Fig. 2-8 shows SEM‘s of an as-released device
and zoomed-in view on the transduction gap. The post-release process used to reduce gap
spacings in this work then consisted of an ALD step using a custom-built system (Fig. 2-9) to
deposit HfO2 into the gaps of already-released disk resonator devices as illustrated in Fig. 2-5.
Then, a simple lithography and HF dip step were performed to remove HfO2 over the bond pads,
followed by photoresist etching in oxygen plasma. The ALD of HfO2 was performed at 140 oC
using tetrakis (ethylmethylamido) hafnium and water vapor prepared at 120 oC.
34
Fig. 2-8: SEM of a fabricated 60 MHz polysilicon wine-glass disk resonator with zoomed-in
view on the ~97 nm transduction gap and the support beam.
Fig. 2-9: A custom-built atomic layer deposition tool for HfO2 deposition, assembled by
Professor Ali Javey‘s research group at UC Berkeley.
2.4.2 Extrapolation of Gap Spacing Before and After ALD
Perhaps the most accurate way to determine the electrode-to-resonator gap spacing for
capacitively transduced resonators is to use advantageously the frequency dependence on VP.
The frequency dependence on VP is a result of nonlinearity inherent to capacitive resonators of
which the vibration amplitude modulates the transduction gap spacing. As the displacement x is
small compared to gap spacing d, performing a Taylor series expansion on the dynamic
capacitance yields
35
C 
C
2
3
4

  o 1  x  2 x 2  3 x 3    
x
d 
d
d
d

(2-15)
Plugging (2-15) into the force equation previously presented in (2-1) and collecting the terms
at ωo results in
F (o )  VP
Co
C
vin (o )  VP2 2o x (o )
d
d
(2-16)
The first term on the right-hand side equals Fωo in (2-2). The second term has the form of spring
restoring force with the equivalent stiffness of
Co
d2
ke  VP2
(2-17)
where ke is usually called the electrical stiffness. Note that (2-17) is for the case of a two
rectangle parallel plate system with displacement orthogonal to the plates. For resonators
vibrating in a wine-glass mode shape, (2-17) no longer holds and needs to be modified to
ke

kr

2
1
1  2  o RHd 
 VP

kr ( ) 
d3 
(2-18)
where kr is the stiffness of the resonator; θ1 and θ2 are the angles of the surrounding electrodes,
as shown in Fig. 2-10(a); other parameters are defined in Fig. 2-8. The electrical stiffness is
subtracted from kr and therefore influences the measured resonant frequency:
fo 
1
2
k m  ke
1

mr
2
km
mr

k
1  e

km





(2-19)
From (2-19) and (2-19), the dependence of measured resonant frequency fo on DC bias
voltage VP is strongly influenced by the gap spacing do, suggesting that plots of fo versus VP can
be used to very accurately extract do.
Fig. 2-11 plots frequency fo versus dc-bias VP for two devices before and after HfO2 coating,
for which curve-fitting with the theoretical prediction of (2-19) yields gaps of 97 nm for the
uncoated disk and 37 nm for the HfO2-coated one — both very close to expectations given that
~30 nm of HfO2 was deposited, all attesting to the precision with which ALD can achieve a
specific film thickness. Note that these theoretical curves are calibrated according to one data
point, as it is difficult to predict the exact resonant frequency given fabrication variability.
However, the resonator frequency has no effect on the curvature, which is used to extract the gap
spacing.
36
θ2
θ1
θ=0
Disk
Gap Spacing d
Fig. 2-10: Arrangement of the electrode surrounding a disk resonator designed for wine-glass
mode vibration.
Using VP dependence on frequency to determine gap spacing is convenient and powerful, as
the gap spacing is obtained from fitting measurement data to the entire theoretical curve for
different VP‗s rather than the absolute values of simulation results. Fig. 2-12 plots similar
measured and theoretical curves for another device after HfO2 ALD, but this time also plotting
the theoretical prediction for a 33 nm gap (dashed line). The offset in the curves at higher applied
VP‘s shows just how sensitive the fo versus VP curve can be in determining gap spacing.
61.3
Frequency (MHz)
61.1
60.9
97 nm Gap Spacing
60.7
60.5
37 nm Gap Spacing
60.3
60.1
Theory
59.9
Measurement
59.7
59.5
0
4
8
12
16
20
24
|VP| (V)
Fig. 2-11: Resonance frequency fo vs. DC bias VP plots of measurement data and theory for a 97
nm gap resonator before and after 30 nm HfO2 coating.
37
59.6
Frequency (MHz)
59.5
33nm gap
by theory
(dashed line)
59.4
59.3
Theory
Measurement
59.2
32nm gap
(solid line)
59.1
59
1
3
5
7
9
11
13
15
|VP| (V)
Fig. 2-12: Resonance frequency fo vs. DC bias VP plots of measurement data and theory for a
32 nm gap partial-filled HfO2 device and the simulated curve for a 33 nm gap device.
2.4.3 Extrapolation of Interconnect Resistance
The resonator model presented in Chapter 1 includes only the motional resistance of the
resonator and leaves out resistance also existing on the signal path during measurement, such as
the contacting resistance of the probe and the bond pad or resistance of the bond wire, and the
interconnect resistance. The interconnect resistance is usually much larger than the rest,
especially for interconnects made of doped semiconductor material, in this case, n+ polysilicon.
Upon resonance, the interconnect resistance is in series with the resonator tank and loads the
resonator Q according to the expression
QMeasure  Q 
Rx
Rx  Rs
(2-20)
where QMeasure is the quality factor measured from the 3 dB width of the resonant peak, Q is the
unloaded quality factor of the resonator, and Rs and Rx are the interconnect resistance and
38
motional resistance, respectively. Interconnect resistance was not a significant issue for the
capacitive resonators demonstrated before as Rs is much less than the resonator motional
impedance Rx. This is no longer the case for resonators equipped with sub-50nm air gaps.
Therefore, precise measurement of interconnect resistance is important to determine the real Q of
the resonator. While it is possible to estimate the interconnect resistance from sheet resistance or
to directly measure it by positioning the probes as close to the electrode as possible, a more
convenient and accurate approach is to use the motional impedance dependence on VP.
The total impedance on the signal path can be calculated from the measured peak height
relative to the 0 dB line, S21, from the expression
Rx  Rs  ( Ri  Ro )(10
 S 21
20
(2-21)
 1)
where Ri and Ro are the input and output impedance of the network analyzer, respectively.
Typically, both Rin and Rout equal 50 Ω. As Rx is inversely proportional to VP2 and Rs is a
constant value for the same measurement setup, the value of Rs can be extrapolated from the
measured (Rx+Rs) value with VP (and VP2) approaching infinity.
Fig. 2-13 plots the measured (Rx+Rs) value against 1/VP2. The y-axis intercept is 600 Ω,
which is the extrapolated value of Rs. Fig. 2-14 plots the simulation curve of Rx versus VP and the
35
VP = 4 V
Rx + Rs (kΩ)
30
25
20
VP = 5 V
15
10
5
VP = 6 V
VP = 7 V
VP = 23 V
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1/VP2 (V-2)
Fig. 2-13: Measured (Rx+Rs) values plotted against inverse of square of VP from which Rs can be
extrapolated from the value of (Rx+Rs) when 1/VP2 approaches to zero.
39
Rx (KΩ)
500
450
400
350
300
250
200
150
100
50
0
VP = 1 V, Rx = 429.4 KΩ
VP = 1.3 V, Rx = 279.5 KΩ
VP = 1.5 V, Rx = 216.0 KΩ
VP = 1.8 V, Rx = 160.0 KΩ
VP = 10 V
Rx = 5.56 KΩ
0
5
10
15
VP = 10 V
Rx = 1.89 KΩ
20
25
VP = 34 V
Rx = 954 Ω
30
35
VP (V)
Fig. 2-14: Simulated curve and measured data of Rx versus VP using Rs = 600 Ω obtained from
Fig. 2-13.
values of Rx obtained by subtracting 600 Ω from the measured data of (Rx+Rs). The consistency
of the theoretical and the measured values confirms that 600 Ω is a good estimation of the series
resistance associated with interconnect and measurement setup.
2.4.4 Measurement Results – Improved FOM
Fig. 2-15 presents the measured frequency response characteristics for a 94 nm-gap wineglass mode disk resonator, with design summarized in Fig. 2-8, and one coated with 30.7 nm of
ALD HfO2 using the process described above in Section 2.3.1, then sintered in forming gas (97%
N2 and 3% H2) at 400˚C for 3 minutes (for reasons to be described later). Here, the measured Q
of the coated resonator is considerably lower than that of the uncoated one—an observation to be
discussed in more detail later. For now, though, accounting for the reduced Q, the extracted e‘s
are 19.84 μC/m and 2.44 μC/m at VP = 16V for the coated and uncoated devices, respectively,
yielding an e improvement of 8.1×, which is very close to the expected 8.6× difference from (26). With an 8.1× increase in e, the filter FOM increases by (8.1)2×=65.6×. The motional
resistance Rx at this point is 966 Ω. Note that the motional impedance Rx is not reduced by the
same ratio as the e increase, as Q is degraded and Rx is inversely proportional to Q according to
(1-3) and (1-11). After another 3 minutes of sintering at 400˚C, the same device achieves Rx=685
Ω and Q = 7,368 at VP = 19 V, as shown in Fig. 2-16.
40
-25
-30
94 nm gap
VP = 16 V
Q = 150,527
Rx = 2.62 kΩ
(a)
-35
S21 (dB)
-40
-45
-50
-55
-60
-65
-70
61.025
61.03
61.035
61.04
61.045
61.05
61.055
Frequency (MHz)
-25
32 nm gap
VP = 16 V
Q = 6,176
Rx = 966 Ω
(b)
-30
S21 (dB)
-35
-40
-45
-50
-55
58.8
58.85
58.9
58.95
59
59.05
Frequency (MHz)
Fig. 2-15: Frequency characteristics of an initially 94 nm gap resonator before and after ALD
coating. (a) right after HF release; (b) after partially filling the gap with 30.7 nm HfO2 and
sintering at 400˚C for 3 minutes, showing Rx < 1 kΩ.
41
-20
32nm gap
VP = 19 V
Q = 7,368
Rx = 685 Ω
-25
S21 (dB)
-30
-35
-40
-45
-50
-55
-60
58.4
58.6
58.8
59
59.2
Frequency (MHz)
Fig. 2-16: Frequency characteristics of an initially 94nm gap resonator after HF release and
partially filling the gap with 30.7 nm HfO2 and sintering at 400˚C for 6 minutes, showing
Q > 10,000. Here, Vp is lower than in Fig. 2-15(b), but all the other parameters are the same.
2.4.5 Methods for Restoring Q
Part of the reason for the reduction in Q seen in Fig. 2-15(b) and Fig. 2-16 derives from the
fact that the Q of a resonator with a smaller Rx is loaded more heavily by parasitic interconnect
resistance than one with a large Rx. But comparisons of Q versus VP plots suggest that more of
the Q reduction derives from interface losses introduced by the HfO2 film. In particular, the same
resonator that achieves Q=6,176 at Vp=16 V, shown in Fig. 2-15(b), is measured with much
higher Q, Q=10,510 at Vp = 5 V, shown in Fig. 2-17. In this respect, the quality of the HfO2
deposited film very likely governs the final Q of an ALD-filled device.
a. Annealing
To gauge the degree with which Q depends upon film quality, ALD-filled devices were
sintered at 400 ˚C in forming gas for varying time periods in order to improve the HfO2 film
quality, as is done for VLSI transistors [22]. Fig. 2-18 presents measured frequency
characteristics for a 61-MHz wine-glass disk resonator with ALD-coated gaps, showing a
marked improvement in Q after 6 minutes of sintering at 350 oC. More work is needed to find the
best recipe, but it appears that a method to restore Q is at least feasible.
42
-35
32nm gap
VP = 5 V
Q = 10,510
Rx = 6.5 KΩ
S21 (dB)
-40
-45
-50
-55
-60
-65
59.25
59.3
59.35
59.4
Frequency (MHz)
59.45
Fig. 2-17: Frequency characteristics of the resonator in Fig. 2-15(b) but with lower Vp, showing
Q > 10,000.
-25
-30
-35
S21 (dB)
-40
Before Sintering
VP = 10 V
fo = 59.052 MHz
Rx = 5.8 kΩ
Q = 1,210
After Sintering
VP = 10 V
fo = 59.150 MHz
Rx = 1.6 kΩ
Q = 7,982
-45
-50
-55
-60
-65
-70
58.75
58.85
58.95
59.05
59.15
59.25
59.35
59.45
Frequency (MHz)
Fig. 2-18: Frequency characteristic of a 37 nm gap resonator before and after sintering, showing
marked improvement in Q, from 1,210 to 7,982, a 6.6 x increase.
43
It should also be noted that the thicker the ALD coating, the lower the Q of a HfO2 ALDcoated disk resonator. Thus, another approach to retaining Q‘s >100,000 for disk resonators is to
merely start with a smaller initial gap and deposit a much thinner ALD coating. For example, if
the initial gaps were 50 nm, then only 9 nm of ALD would be needed to match the 32 nm gaps of
this work, and the Q should be higher.
Although annealing enhances Q, the effective gap spacing appears to increase after
annealing. In particular, the gap spacing of the resonator in Fig. 2-18 is measured using the
method described in section 2.3.2 before and after annealing and show 32 nm and 38 nm,
respectively, as plotted in Fig. 2-19. This explains why the Rx reduction is only 3.6x, instead of
6.6x, with 6.6x improvement in measured ‗unloaded‘ Q before and after annealing, shown in Fig.
2-18. Three possible scenarios, or any combination of them, as drawn in Fig. 2-19, can cause the
effective gap spacing to increase after annealing: first, the physical thickness of HfO 2 decreases,
i.e., the film becomes denser; second, the dielectric constant of HfO2 decreases, contributing to
larger effective air gap spacing; third, an interfacial layer forms from the HfO2-silicon interface
into the polysilicon such that the total dielectric thickness increases.
Frequency (Hz)
The first scenario, a change in physical HfO2 film thickness, is tested out by measuring the
step height change of patterned HfO2 on polySi films before and after the same annealing
conditions. To ensure that the step height change, if any, is well above the resolution of the
profilometer used for step height measurement, patterned 120 nm thick HfO2 is subjected to the
same annealing conditions. If a change in physical HfO2 film thickness is solely responsible for
the effective air gap increase, based on Fig. 2-19, 30.7nm thick HfO2 decreases to 27.7 nm after
annealing. If the densification ratio is the same for thin and thicker films, 120 nm thick HfO2
should exhibit a step height change of 11.7 nm after annealing. However, no change in step
59.4
59.35
59.3
59.25
59.2
59.15
59.1
59.05
Theoretical Curve
for 38 nm Gap
Measured Data
Before Sintering
After Sintering
Theoretical Curve
for 32 nm Gap
0
2
4
6
8
VP (V)
10
12
14
Fig. 2-19: The effective gap spacing changes from 32 nm to 38 nm after 6 minutes of sintering at
350oC. This explains why the impedance reduction is not as much as the Q improvement in Fig.
2-18.
44
(a)
(c)
dcoat
dair
dair
d'air
(b)
dcoat
dcoat
d'air
d'air
(d)
Fig. 2-20: (a) the partial-filled gap before sintering with effective gap spacing of 32 nm; (b)-(c)
three scenarios that can cause the effective gap spacing to increase to 38 nm after annealing: (b)
physical thickness of ALD film decreases by ~3 nm on each side; (c) dielectric constant of the
ALD film drops such that the ALD film contributes to extra effective air gap spacing; (d)
interfacial layer with lower dielectric constant than HfO2 forms at the HfO2-poly-Si interface.
height is observed.
Next, the second scenario is considered, where the increase of the effective gap spacing is
caused by a decrease in the dielectric constant of HfO2. A 6 nm difference in gap spacing, or 3
nm difference from 30.7nm HfO2 film on each side, corresponds to a dielectric constant change
from the original value of 18 to ~6.5. No literature has been found which reports such a dramatic
reduction in dielectric constant. Instead, some literature reports that the dielectric constant
increases as the annealing temperature increases as the annealing temperature increases [28]. It is
therefore unlikely that the effective gap spacing increase after annealing is entirely due to a drop
in the dielectric constant of HfO2.
On the other hand, the work in [29] investigated the thermal stability of thin ALD HfO2 films
and suggested the formation of an interfacial layer at HfO2-Si interface as the main cause of
increased capacitance equivalent oxide thickness (CET) after anneal at 700 °C in nitrogen. In
particular, for HfO2 with physical thickness of ~4.5 nm, the CET is ~0.7 nm (using dielectric
constant of 25 and 4 for HfO2 and SiO2, respectively) before annealing and increases to 0.9 nm
and 1.3 nm after 10 seconds and 15 seconds of annealing, respectively, at 700 °C. Such a large
increase in CET is similar to what has been observed in the effective gap spacing increase shown
in Fig. 2-19. X-ray photoelectron spectroscopy (XPS) further reveals the formation of an
interfacial layer at the interface, which is likely to contribute to the CET increase [29].
45
HfO2
Electrode
HfO2
Suspended Disk
Suspended Disk
(a)
(b)
Fig. 2-21: (a) a short HF etching is expected to remove HfO2 above and below the disk resonator
without removing HfO2 in the high-aspect-ratio lateral transduction gaps due to limited mass
transportation rate; (b) what is possibly the actual case, where HfO2 remains underneath the disk.
b. Remove Undesired HfO2 Film
The ALD process coats every exposed surface with HfO2, but only the HfO2 film in the
transduction gap contributes to coupling enhancement. HfO2 on top of and beneath the disk
resonator does not help reduce the gap spacing; even worse, it dissipates energy, thus causes
lower Q. Another approach for improving Q is to retain the HfO2 film only in the transduction
gap and to remove HfO2 from the other areas. This could be achieved by taking advantage of the
much slower etching rate for materials in a high aspect ratio trench (i.e., the transduction gap)
due to limited mass transportation rate. A HF etch with optimal etching time may render a cross
section like Fig. 2-21(a). Unfortunately, no resonant peak was measured after short HF etching.
A possible failure mechanism is the unbalanced stress imposed on the disk resonator by the
remaining HfO2 underneath the disk if only HfO2 above the disk is removed, resulting in the
cross section in Fig. 2-21(b).
c. Reduce surface loss via barrier layer
There are two approaches for minimizing the energy dissipation at the interface of polysilicon and ALD films, which can be the main cause of lower Q. One approach is to minimize
the energy dissipation per unit area of the interface; another approach is to minimize the total
interface area. This and the next subsection discuss the first and the second approaches,
respectively.
The purpose of the barrier layer is to better prepare the rather rough poly-silicon surface,
especially on the dry etched sidewalls, for ALD. It can also ensure good thermal stability of the
device with ALD coating by serving as a blocking layer for inter-diffusion of silicon and atoms
which are mobile at elevated temperatures. In practice, this barrier layer can be only a few
monolayers thick and can comprise either dielectric or metal. This concept has been
demonstrated in [30] by using 3 nm Al2O3 as the barrier layer for 25 nm thick TiO2. Al2O3 can be
deposited on silicon without special surface treatment [31] – an advantage over TiO2. Q
improvement of 1.35 x is achieved compared to identical devices with ALD Al2O3 coating alone.
46
d. Reduce surface loss via smoother surface
The zoomed-in SEM in Fig. 2-8 shows the surface roughness along the sidewalls of the polySi disk. A rough surface increases the total poly-Si and high-k dielectric interface areas, as ALD
is extremely conformal. While it is possible to reduce the sidewall roughness by optimizing the
dry etch recipe, a more efficient way is perhaps to reflow silicon to smooth the surface.
Annealing in a hydrogen-rich environment to enable silicon reflow has been applied to numerous
applications, including packaging [32], eliminating the scalloping of silicon trenches created by
deep reactive ion etch (DRIE) and 3D features for MEMS [33], smooth surfaces of optical
waveguides [34], and smoother sidewall of the FinFET [35]. Note that all of the above examples
mobilize silicon atoms in a single crystal silicon substrate; little has been reported on applying
the same annealing step to polycrystalline silicon. This approach for improving Q of ALD highk-dielectric-coated resonators has not yet been experimentally confirmed.
2.4.6 Dielectric Charging
In addition to Q-reduction, another concern regarding dielectric-partial-filled devices is
charging. In particular, any ‗net‗ charge in the ALD oxide, or at the oxide-silicon interface, will
impose a change in electrical stiffness that will pull the frequency of the resonator up or down,
according to the sign of the net charge and the polarity of VP. The existence of such charge is
discernable by comparing plots of fo versus VP, one with positive VP, another with the polarity of
the VP reversed (i.e., with VP = -VP). Here, a shift in the curve identifies the presence of charge.
Based on the electric stiffness equation of (2-18) and (2-19), the amount of the ‗net‘ change can
be calculated from the frequency shift when the polarity of VP is reversed. Related equations
have been derived in [36] and will not be repeated here.
Fig. 2-22 presents plots of fo versus VP and reverse polarity VP for a partial-ALD-filled gap
device before and after sintering at 400oC in forming gas (97% N2 and 3% H2) for 3 minutes.
Before sintering, the curve of positive VP is horizontally right-shifted from that of negative VP,
while no difference is seen after sintering. It seems that sintering is a very effective means by
which to virtually eliminate the oxide charging issue, at least for HfO2 ALD gap coatings.
47
(MHz)(MHz)
Frequency
Frequency
59.4
-VP
VP
-VP
59.25
59.3
59.2
59.25
59.15
59.2
59.1
59.15
59.05
59.1
59.05
(MHz)(MHz)
Frequency
Frequency
VP
59.35
59.4
59.3
59.35
∆f
∆f
(a)
2 (a) 3
2
3
59.4
59.38
59.4
59.36
59.38
59.34
59.32
59.36
59.3
59.34
59.28
59.32
59.26
59.3
59.24
59.28
59.22 (b)
59.26
59.2
59.24
59.22 2 (b) 3
59.2
2
3
4
5
6
7
8
9
10
11
8
9
10
11
|VP| (V)
4
5
(a)
6
7
|VP| (V)
VP
-VP
VP
-VP
4
5
6
7
8
9
10
11
8
9
10
11
|VP| (V)
4
5
6
7
|VP| (V)
(b)
Fig. 2-22: Resonance frequency fo vs. dc-bias VP plots of a 32 nm gap resonator (a) before
sintering; and (b) after sintering.
48
2.5 References
[1] Y.-W. Lin, L.-W. Hung, S.-S. Li, Z. Ren, and C. T.-C. Nguyen, ―Quality factor boosting via
mechanically-coupled arraying,‖ Dig. of Tech. Papers, the 14th Int. Conf. on Solid-State
Sensors & Actuators (Transducers‘07), Lyon, France, June 11-14, 2007, pp. 2453-2456.
[2] S.-S. Li, Y.-W. Lin, Y. Xie, Z. Ren, and C. T.-C. Nguyen, ―Micromechanical ―hollow-disk‖
ring resonators,‖ Proceedings, 17th Int. IEEE Micro Electro Mechanical Systems Conf.,
Maastricht, The Netherlands, Jan. 25-29, 2004, pp. 821-824.
[3] D. Weinstein1 and S. A. Bhave, ―Acoustic resonance in an independent-gate FinFET,‖ Tech.
Digest, Solid-State Sensor, Actuator, and Microsystems Workshop, Hilton Head, South
Carolina, 2010, pp. 459-462.
[5] S.-S. Li, Y.-W. Lin, Z. Ren, and C. T.-C. Nguyen, ―An MSI micromechanical differential
disk-array filter,‖ Dig. of Tech. Papers, the 14th Int. Conf. on Solid-State Sensors &
Actuators (Transducers‘07), Lyon, France, June 11-14, 2007, pp. 307-311.
[6] Y. Xie, S.-S. Li, Y.-W. Lin, Z. Ren, and C. T.-C. Nguyen, "1.52-GHz micromechanical
extensional wine-glass mode ring resonators," IEEE Trans. Ultrason., Ferroelect., Freq.
Contr., vol. 55, no. 4, pp. 890-907, April 2008.
[7] L.-W. Hung, Z. A. Jacobson, Z. Ren, A. Javey, and C.T.-C. Nguyen, ―Capacitive transducer
strengthening via ALD-enabled partial-gap filling,‖ Tech. Digest, Solid-State Sensor,
Actuator, and Microsystems Workshop, Hilton Head, South Carolina, 2008, pp. 208-211.
[8] D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, ―Atomic layer deposition of
hafnium and zirconium oxide using metal amide precursors,‖ Chem. Mater., vol. 14, 2002,
pp. 4350-4358.
[9] Y.-W. Lin, S.-S. Li, Z. Ren, and C. T.-C. Nguyen, ―Vibrating micromechanical resonators
with solid dielectric capacitive transducer gaps,‖ Proceedings, Joint IEEE Int. Frequency
Control/Precision Time & Time Interval Symposium, Vancouver, Canada, Aug. 29-31,
2005, pp. 128-134.
[10] A. I. Zverev, Handbook of Filter Synthesis. NY: Wiley, 1967.
[11] F. D. Bannon III, J. R. Clark, and C. T.-C. Nguyen, ―High-Q HF microelectromechanical
filters,‖ IEEE J. Solid-State Circuits, vol. 35, no. 4, pp. 512-526, April, 2000.
[12] M. Demirci and C. T.-C. Nguyen, ―Mechanically corner-coupled square microresonator
array for reduced series motional resistance,‖ IEEE/ASME J. Microelectromech. Syst., vol.
15, no. 6, pp. 1419-1436, Dec. 2006.
[13] H. Chandrahalim, D. Weinstein, L. F. Cheow, and S. A. Bhave, ―Channel-select
micromechanical filters using high-k dielectrically transduced resonators,‖ Technical Digest,
Int. IEEE Micro Electro Mechanical Systems Conference, 2006, pp. 894-897.
[14] R. Navid, J. R. Clark, M. Demirci, and C. T.-C. Nguyen, ―Third-order intermodulation
distortion in capacitively-driven CC-beam micromechanical resonators,‖ Technical Digest,
49
Int. IEEE Micro Electro Mechanical Systems Conference, Interlaken, Switzerland, Jan. 2125, 2001, pp. 228-231.
[15] H. Takeuchi, E. Quévy, S. A. Bhave, T.-J. King, and R. T. Howe ―Ge-blade damascene
process for post-CMOS integration of nano-mechanical resonators,‖ IEEE ELECTRON
DEVICE LETTERS, vol. 25, no. 8, August 2004, pp. 529-531.
[16] Y.-W. Lin, S.-S. Li, Z. Ren, and C. T.-C. Nguyen, ―Low phase noise array-composite
micromechanical wine-glass disk oscillator,‖ Technical Digest, IEEE Int. Electron Devices
Mtg. (IEDM), Washington, DC, Dec. 5-7, 2005, pp. 287-290.
[17] K. Hamaguchi, T. Tsuchiya, K. Shimaoka, and H. Funabashi, "3-nm gap fabrication using
gas phase sacrificial etching for quantum devices," Technical Digest, Int. IEEE Micro
Electro Mechanical Systems Conference, 2004, pp. 418-421.
[18] T. J. Cheng and S. Bhave, ―High-Q, low impedance polysilicon resonators with 10nm air
gaps,‖ Technical Digest, Int. IEEE Micro Electro Mechanical Systems Conference, 2010,
pp. 695-698.
[19] M. A. Sahiner, J. C. Woicik, P. Gao, P. McKeown, M. C. Croft, M. Gartman, and B.
Benapfla, "Pulsed laser deposition and characterization of Hf-based high-k dielectric thin
films," J. of Thin Solid Films, vol. 515, pp. 6548-6551, 2007.
[20] B.-Y. Tsui and H.-W. Chang, ―Formation of interfacial layer during reactive sputtering of
hafnium oxide,‖ J. Appl. Phys. vol. 93, vol. 12, pp. 10119-10124, 2003.
[21] S. Sayan, S. Aravamudhan, B. W. Busch, W. H. Schulte, F. Cosandey, G. D. Wilk, T.
Gustafsson, E. Garfunkela, ―Chemical vapor deposition of HfO2 films on Si (100),‖ J. Vac.
Sci. Technol. , Mar/Apr, 2002, pp.-507-512. …
[22] D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, ―Atomic layer deposition of
hafnium and zirconium oxides using metal amide precursors,‖ Chem. Mater. 2002, 14,
4350-4358.
[23] K. Kukli, M. Ritala, T. Sajavaara, J. Keinonen, M. Leskela, ―Atomic layer deposition of
hafnium dioxide films from hafnium tetrakis (ethylmethylamide) and water,‖ Chem. Vap.
Deposition, vo. 5, pp. 199-204, 2002.
[24] M. Onoe, ―Contour vibrations of isotropic circular plates,‖ J. of the Acoustical Society of
America, vol. 28, no. 6, pp. 1158-1162, Nov. 1956.
[25] Y.-W. Lin, S. Lee, S.-S. Li, Y. Xie, Z. Ren, C. T.-C. Nguyen, ―Series-resonant VHF
micromechanical resonator reference oscillators,‖ IEEE J. of solid-state circuits, vol. 39, no.
12, 2004, pp. 2477-2491.
[26] J. Wang, Z. Ren, and C. T.-C. Nguyen, ―Self-aligned 1.14-GHz vibrating radial-mode disk
resonators,‖ Dig. of Tech. Papers, the 12th Int. Conf. on Solid-State Sensors & Actuators
(Transducers‘03), Boston, Massachussets, June 8-12, 2003, pp. 947-950.
[27] S. W. Jeong, H. J. Lee, K. S. Kim, M. T. You, Y. Roh, T. Noguchi, W. Xianyu, and J. Jung,
"HfO2 gate insulator formed by atomic layer deposition for thin-film-transistors," Thin Solid
Films, vol. 515, pp. 5109-5112, 2007.
50
[28] S. W. Jeong, H. J. Lee, K. S. Kim, M. T. You, Y. Roh, T. Noguchi, W. Xianyu, and J. Jung,
"Effects of annealing temperature on the characteristics of ALD-deposited HfO2 in MIM
capacitors," Thin Solid Films, vol. 515, pp. 526-530, 2006.
[29] B. H. Lee, L. Kang, R. Nieh, W.-J. Qi, and J. C. Lee. ―Thermal stability and electrical
characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal
annealing,‖ Appl. Phys. Lett. vol. 76, pp. 1926-1928, 2000.
[30] M. Akgul, B. Kim, Z. Ren, and C. T.-C. Nguyen, ―Capacitively transduced micromechanical
resonators with simultaneously low motional resistance and Q>70,000,‖ Tech. Digest, SolidState Sensor, Actuator, and Microsystems Workshop, Hilton Head, South Carolina, 2010,
pp. 467-470.
[31] A. C. Dillon, A. W. Ott, J. D. Way, and S. M. George, "Surface chemistry of Al 2O3
deposition using Al(CH3)3 and H2O in a binary reaction sequence," Surface Science, vol.
322, pp. 230-242, 1995.
[32] S. Sedky, H. Tawfik, A. Abdel Aziz, S. ElSaegh, A. B. Graham, J. Provine, and R. T. Howe,
‗Low thermal-budget silicon sealed-cavity microencapsulation process,‘ Technical Digest,
Int. IEEE Micro Electro Mechanical Systems Conference, 2011, pp. 276-279.
[33] M. C. M. Lee and M. C. Wu, "Thermal annealing in hydrogen for 3-D profile transformation
on silicon-on-insulator and sidewall roughness reduction," Microelectromechanical Systems,
Journal of, vol. 15, pp. 338-343, 2006.
[34] F. Gao, Y. Wang, G. Cao, X. Jia, and F. Zhang, ‗reduction of sidewall roughness in siliconon-insulator rib waveguides,‘ J. of Applied Surface Science 252, 2006, 5071–5075.
[35] R. J. Zaman, W. Xiong, R. Quintanilla, T. Schulz, C. R. Cleavelin, R. Wise, M. Pas, P.
Patruno, K. Schruefer and S. K. Banerjee, ‗Effects of hydrogen annealing process conditions
on nano scale silicon (011) fins,‘ in Proc., Mater. Res. Soc. Symp., vol. 872, pp. J3.1.1J3.1.5, 2005.
[36] G. Bahl, R. Melamud, B. Kim, S. A. Chandorkar, J. C. Salvia, M. A. Hopcroft, D. Elata, R.
G. Hennessy, R. N. Candler, R. T. Howe, T. W. Kenny, ‗Model and observations of
dielectric charge in thermally oxidized silicon resonators,‘ IEEE/ASME J.
Microelectromech. Syst., vol. 19, no. 1, 2004, pp. 162-174.
51
Chapter 3: Silicide-Induced Gaps
3.1 Fabrication of High Aspect Ratio Microstructures
3.1.1 Need for High Aspect Ratio Microstructures
From the view point of fabrication, the aspect ratio of a released or suspended microstructure
can be defined as the ratio of the largest to the smallest dimensions of the released gap spacing.
As an example, for a square diaphragm which has lateral dimension W on each side and is
suspended H distance above the substrate, the aspect ratio is W/H. High aspect ratio structures
are useful in many ways, including but not limited to:
1. The coupling coefficient of a capacitive transducer force is inversely proportional to the
square of the transduction gap spacing. Large coupling coefficients are desirable for
applications where low impedance of resonators, high sensitivity of sensors, or large
actuation forces of actuators are essential. For example, the aspect ratio reaches 1,000 for
a diaphragm that is 10 µm wide and suspended 10 nm above the substrate.
2. Some applications require either more compliant microstructures or larger mass, which
usually require larger lateral dimensions. Applications like these can be found in
accelerometer proof masses and pressure sensor diaphragms. Although small gap spacing
may not be necessary, the resulting aspect ratio remains high due to large lateral
dimensions. For example, the aspect ratio is 1,000 for a diaphragm that is 1,000 µm wide
and suspended 1 µm above the substrate.
3. Many MEMS sensors offer better sensitivity than their macro-scale counterparts due to
the much larger surface to volume ratio achievable when the devices are scaled down to
micrometer scale. The surface to volume ratio of a channel or a tube increases as the
radius decreases, therefore the aspect ratio increases.
Very often, the bottleneck of fabricating high aspect ratio microstructures lies in the
difficulty in forming high aspect ratio gaps or releasing the microstructures. The following
sections discuss the three most common approaches forming high aspect ratio gaps and the
related issues. The discussions in this chapter focus on high aspect ratio microstructures made of
non-polymer material. As a side note, many methods have been developed to form high aspect
ratio polymer structures, such as hot embossing and LIGA process.
3.1.2 Wafer Bonding
Intuitively, a suspended microstructure can be fabricated by bonding two pieces together [1].
This is accomplished by either bonding a recessed microstructure to a flat substrate as illustrated
in Fig. 3-1(a) and demonstrated in [2], or bonding a microstructure to a recessed substrate, as
illustrated in Fig. 3-1(b) and demonstrated in [3]. The patterning of the microstructures can be
performed either before or after the bonding process. Although the concept is straightforward,
this method has inherent limitations:
52
First, most bonding processes require elevated temperatures or pressures. The induced
thermal and mechanical stresses during and after the bonding process can fail the suspended
microstructures, especially the compliant ones. Techniques for bonding wafers with limited
thermal budget have been improved dramatically, thanks to the efforts pursuing heterointegration for MEMS and readout circuitry and, recently, 3D integration to continually increase
transistor density. Bonding processes for silicon wafers at temperatures less than 400 °C and
with low to moderate bonding pressure typically utilizes an intermediate layer, ranging from
polymer adhesives [4] such as parylene [5], melting glass [6], and metals at eutectic temperatures
[3].
The control and the minimum requirement on thickness of the intermediate layer affects the
minimum achievable gap spacing beneath the suspended structure resulted from wafer bonding.
It is therefore difficult to scale the uniform gap spacing down to less than 50 nm, as needed by
the electrostatic transducers.
Moreover, the bonding rim surrounding the suspended structures is usually > 50 µm wide to
ensure sufficient bonding strength and to accommodate misalignment during the bonding
process. While a > 50 µm wide bonding rim is not a significant problem for devices with
dimensions as large as 500 µm, such as the silicon diaphragm in [7], it consumes a relatively
large silicon footprint for devices of only 50 µm wide or smaller. The excess demand for space is
even worse if the MEMS suspended structures are fabricated directly on a CMOS chip via low
temperature bonding. Wafer bonding is good for MEMS structures with lager dimensions and
when only a few of them are required on a functional chip. It is not a useful solution for many
small devices needed to work together as a functional unit. In other words, wafer bonding is not
an easily scalable process. Finally, the bonding process shown in Fig. 3-1 cannot be applied to
form lateral gaps.
3.1.3 Direct Dry Etching
Another approach is to directly define the gap spacing by anisotropic etching. A comb-drive
resonator [8] (Fig. 3-2(a)) is an example of using anisotropic etching to define the gap spacing
between each comb-drive finger functioning as capacitive transducers. The achievable minimum
gap spacing is limited by how anisotropic the etching is. Among all of the known methods for
etching silicon, deep reactive ion etch (DRIE) offers the most anisotropic etching.
DRIE was developed in 1994 by Bosch, where alternation of polymer passivation cycles and
etching cycles results in silicon trenches with high aspect ratios unachievable using previous
(a)
(b)
Fig. 3-1: A suspended microstructure can be formed by either (a) bonding a recessed and
patterned wafer to a flat substrate, or (b) bonding a patterned water to a recessed substrate.
53
reactive ion etch (RIE) techniques. This process has since become one of the most important
processes of enabling MEMS technologies based on silicon. DRIE is also useful for fabricating
through silicon wafer vias (TSV) and high density capacitors for dynamitic random access
memory (DRAM). Some variations of the original Bosch DRIE process have resulted in aspect
ratios of 107:1 and 40:1 for 374 nm wide and 130 nm wide trenches, respectively [9][10] (Fig. 32(b)). The achievable aspect ratio is expected to be lower with even smaller trench openings. The
gap spacing of the wine-glass disk resonators presented in Chapter 2 have an effective gap
spacing of 32 nm and a disk height of 3 µm, resulting in an aspect ratio of 94:1, which is much
higher than the achievable aspect ratio of current silicon etching technologies.
3.1.4 Release by Etching Sacrificial Materials
Release processes, whereby sacrificial material between two structural materials is removed
to free them from one another, often comprise the most limiting and costly steps in MEMS
fabrication. Such processes generally employ liquids or gases to etch and are fraught with
numerous perils, including
1. Stiction [11]: The stiction failures of MEMS devices are related to the capillary force when
the release occurs in a wet environment. Logically, absence of the liquid-gas interface
eliminates the capillary pull force. Methods for anti-stiction release based on this idea include
critical point drying and dry etching. In the former approach, liquid CO2 gradually replaces
the rinse solution, e.g., methanol or IPA, at elevated pressures and eventually is taken to the
critical point of CO2 where the liquid-gas interface does not exist. Dry etch, on the other
hand, avoids liquid all together. Examples of isotropic dry etch include using vapor HF to
etch oxide, using XeF2 to etch silicon, germanium, molybdenum, using oxygen plasma to
etch sacrificial polymers, and using SF6 to etch silicon.
2. Diffusion-limited etch rate: To react with the sacrificial material within a trench, etchants
need to diffuse to the etch front. For long trenches, the diffusion process governs the etch rate
with a time dependence of t-0.5 [12], similar to the diffusion-limited thermal oxidation rate
Fingers
(a)
(b)
Fig. 3-2: (a) SEM of a comb-drive resonator in [8]; (b) Tunable optical filter consisting of two
free standing vertical distributed Bragg reflector (DBR) mirrors demonstrated in [9]. The high
aspect ratio DBR is fabricated by DRIE with air gap spacing defined by the direct etching.
54
modeled by the Deal-Grove model. As the gap aspect ratio increases, the required etch time
increases. The need for longer etch time, combined with limited etch selectivity among
materials for any etching process, limits the geometry of releasable microstructures.
3. The attack of unintended layers due to finite etchant selectivity and the formation of etch byproducts (e.g., bubbles, residuals) that remain in the gaps.
These yield-limiting phenomena often force alterations in MEMS designs (e.g., release holes)
that compromise the performance of applications employing high-aspect ratio gaps. Indeed, the
set of affected applications is quite large, from inertial sensors that must incorporate massreducing etch holes into their proof masses to speed up the release process [13]; to sealed
encapsulation chambers, many of which are achieved via cap-to-wafer bonding methods rather
than more area-efficient film deposition strategies [14], since the latter often ending up requiring
lengthy etches to release structures within the encapsulation; to GHz high-Q mechanical
resonators [15], for which the size of the electrode-to-structure gap spacing needed to achieve
low impedance and good power handling is limited nearly entirely by the release etch process.
This work erases such limits by introducing a new method for forming high aspect ratio gaps
between movable (or immovable) structures that avoids etching and its associated drawbacks,
entirely. Instead, the method here employs a self-sufficient silicide chemical reaction to provide
volume shrinkage which then induces a gap between surfaces involved in the reaction. Using
this silicide-based approach, 100×100 m2 membranes with membrane-to-substrate gaps of only
385 nm—a 260:1 lateral dimension-to-vertical gap aspect ratio—have been released in only 2
minutes, which is much shorter than the 40 minutes or more that would be required to wet-etch a
385 nm sacrificial oxide under a membrane of similar size. In addition, 32.5 nm gaps have been
formed between a SiGe film and a silicon substrate, verifying the efficacy of this method for
attaining sub-50nm gaps, as needed for capacitive RF micromechanical resonators.
3.2 Silicide-Induced Gaps
3.2.1 Better Ways for Forming Internal Gaps
The etch-based release is plagued by limited diffusion paths and limited etch selectivity of
sacrificial materials over other materials also exposed to the etchant. To address these issues,
researchers have tried to enhance the etch selectivity by using different sacrificial materials, such
as using cross-linked PMMA [16] and polymer [17] for which isotropic oxygen plasma etching
can release the device; by changing the etching conditions, such as the chemical compositions of
the etchant and etching temperatures. Researchers also tried to increase the etchant diffusion rate
by replacing liquid etchants with gaseous etchant, and to facilitate easier access to the etch frontend by employing release holes to the microstructures. However, the need for mass
transportation and finite etch selectivity is inherent to any etching process; the achievable aspect
ratio of the microstructures is therefore always limited, as long as etching is required to release
the microstructures.
The key recognition behind the present work is that etching is not needed to form a gap.
Rather, a gap can also form if a method is available for shrinking the volume of a submerged
layer. It is desirable if the reaction used in this method also exhibits the following features:
55
1. The reaction is self-sufficient such that all of the reactants present on the wafer and the
products of the reaction remain on the wafer. This self-sufficient property eliminates the
need for diffusion paths, therefore eliminating the root of the problem that plagues etchbased release processes.
2. All of the reaction and the products are solid-phase. This solid-phase property enables the
ability of forming a vacuum within the sealed cavity after the reaction as no gaseous
products are generated.
3. This reaction is activated only at specific conditions. This property ensures that the
wafers can be processed as usual and the gaps are formed only at the last step of
fabrication upon subjection to a specific process condition. Examples of possible
controllable process conditions are temperature, pressure, or PH value.
4. The reaction only happens with specific material pairing. This material pairing property
ensures that when the wafer is subjected to proper process conditions to start this
reaction, gaps only form at places with suitable material pairing by design. This is
analogous to the ‗selectivity‘ associated with this reaction.
5. As the self-sufficient property dictates that all the reactants present and products remain
on the wafer, both the reactants and products need to be common materials for MEMS
and solid-state transistors.
6. This reaction must be compatible to transistor fabrication, cost-effective, suitable for
mass production, and can be performed in a standard microfabrication tool.
One reaction that satisfies the above criteria is silicidation, whereby silicon, the most
commonly used material in CMOS and MEMS, reacts under elevated temperatures with a variety
of metals to form silicides.
3.2.2 A Brief Introduction to Silicidation
Silicides are widely used in electronic devices to reduce contact resistance. Silicides can be
formed by either a solid-state reactive diffusion between the metal and Si or by co-sputtering the
metal and Si. Of particular interest here are the refractory metal silicides formed in the selfaligned silicidation, or salicide, process by rapid thermal annealing (RTA). Salicide process has
been commonly used to form low-resistance contacts to the terminals of field effect transistors
(FETs), i.e., gates, sources, and drains. Fig. 3-3 illustrates different steps of a typical salicide
process. After the polysilicon gate and source/drain junctions are fabricated, shown in Fig. 33(a), a conformal blanket of metal is deposited onto the structure (Fig. 3-3(b)), followed by rapid
thermal annealing to form silicide. At the silicidation temperature, the metal reacts with only the
underlying polysilicon but not the dielectric, resulting in the cross-section in Fig. 3-3(c). Finally,
a selective wet etch removes the un reacted metal on the dielectric and does not etch much or any
of the silicide formed over the contact areas, shown in Fig. 3-3(d).
Table 1 [18] lists properties of some common silicides where the metal reacts with single
crystal silicon. Depending on the type of metal used and the particular phase of silicide formed,
the silicidation temperature ranges from 350 °C for nickel silicide up to 800 °C for titanium
silicide.
56
Dielectric
Spacer
Source
Gate
Field
Oxide
Metal
Drain
Gate
Field
Oxide
Silicon
Silicon
(a)
(b)
Unreacted
Metal
Silicide
Silicide
Gate
Gate
Silicon
Silicon
(b)
(d)
Fig. 3-3: (a) Fabricated polysilicon gate, dielectric sidewall spacers, source and drain; (b)
deposition of conformal blanket metal; (c) thermal treatment, typically rapid thermal annealing at
silicidation temperature, to form silicide selectively; (d) wet etch to selectively remove unreacted metal over dielectric and other materials.
Table 3-1: Properties of common silicides
Silicide
Ni2Si
NiSi
TiSi2
PtSi
CoSi2
MoSi2
Silicidation Temp.
~250C
~400˚C
~850˚C
~500˚C
~750˚C
~750˚C
tSi
0.91
1.84
2.30
1.30
3.60
2.56
tsili
1.47
2.22
2.50
1.95
3.53
2.59
tsi = nm of Si consumed per nm of metal (tm=1)
tsili = nm of silicide formed per nm of metal (tm=1)
δ = nm of step height change per nm of metal (tm=1)
57
Volume Shrinkage
23.0%
21.8%
24.1%
15.1%
23.2%
27.25%
δ
0.44
0.62
0.8
0.35
1.07
0.97
3.2.3 Silicide-Induced Gaps
Table 3-1 also shows the theoretical volume ratio of consumed metal to silicon for different
silicides. The data also includes information gauging the amount of ―volume shrinkage‖ afforded
by a given silicidation reaction, assuming a starting metal sitting flush atop a silicon substrate, as
illustrated in the schematic above Table 3-1. Specifically, the combined thickness of the metal
and the silicon consumed is less than the thickness of the silicide formed. As a result, the step
height decreases after the silicide forms.
Fig. 3-4 illustrates one method by which silicidation can be used to form a submerged gap.
Here, 10nm of molybdenum (Mo) is sandwiched between silicon (Si) below and a capping layer
of oxide above. Upon heating via rapid thermal annealing in a low oxygen environment, the Mo
and Si react to form MoSi2, whereby 10x2.56 = 25.6 nm of silicon is consumed to form 10x2.59
= 25.9 nm of MoSi2. This means the step height changes from the 10nm original metal thickness
to now only 25.9-25.6 = 0.3 nm, leaving a 10-0.3 = 9.7 nm gap between the top of the silicide
and the bottom of the oxide cap.
Oxide
10nm Mo
Oxide
Anneal
9.7nm Gap
25.9nm Silicide
Si Substrate
25.6nm Si
consumed
Si
Fig. 3-4: Schematic of how to form a submerged gap using the volume reduction property of Mo
silicide.
The advantages of this silicide-based approach over etch-based release processes are
numerous and include:
1) Greatly reduces the time needed for release, since the time required is governed by a single
interface reaction time rather than by lateral transport rates.
2) Avoids damage to structures not involved in the release, which is an important limiting sideeffect of sacrificial layer-based approaches, where the etchant used often has a finite
selectivity to other surrounding layers.
3) Avoids surface tension-based sticking or problems with bubble formation during release that
commonly plague wet release approaches.
4) Allows the formation of gaps in sealed chambers (i.e., no need for access routes).
58
3.3 Experimental Results
3.3.1 Demonstration of Silicide-Induced Gaps
Fig. 3-5 and Fig. 3-6 summarize processes used for basic demonstration of silicide-induced
gaps. In Fig. 3-5, 200 nm of sputtered molybdenum is patterned by wet etching into strips,
followed by 600 nm of PECVD capping oxide deposited at 300 ˚C. After just 1 minute of
annealing at 750 ˚C, a gap forms when volume shrinkage during silicidation pulls the silicided
surface away from the capping oxide. The rounding at the gap edges results from rounding of the
original metal corners during isotropic wet etching. The gaps essentially take on the shape of the
metal layer, and the shape of silicide is a mirror image of the metal relative to the silicon surface.
The process of Fig. 3-6 differs from that of Fig. 3-5 only in the use of a semiconductor top
layer, where PECVD amorphous silicon is used instead of oxide. Otherwise, the silicidation
procedure is essentially the same, except that now silicides form on both the top and bottom
surfaces of the gap. This process has the advantage of allowing a conductive semiconductor
structural material, which is needed for electrostatic transduction. For applications where
silicidation at the bottom of the conductive microstructure is not desired, (e.g., due to stress
imbalance issues), it can be prevented by depositing a thin layer of dielectric between the
microstructure and the metal, similar to the thin sidewall spacers used in CMOS to prevent
silicidation on the polysilicon gate [19]. For applications where sub-10 nm dielectric layers can
compromise device performance, such as capacitively transduced high-Q resonators and
switches, conductive materials that do not react with metal at the silicidation temperatures can be
used as structural layers. Some good candidates include doped silicon carbide, doped
polycrystalline diamond, or metals with higher silicidation temperatures.
It should be noted that this method is not suitable for forming >1 µm gap spacing for two
reasons. First, it is challenging to deposit blanket metal films thicker than 1 µm without excess
residual stress and vertical stress distribution, which can cause non-uniform silicide and therefore
non-uniform gap spacing. Second, silicidation introduces stress to the reactant silicon, either the
silicon substrate or the silicon microstructures or both, due to volume change, lattice mismatch,
and thermal stress. The latest is the dominating factor for silicide formed at higher temperatures.
In this case, a metal film is deposited and reacts with silicon in a stress-free state at higher
temperatures and subsequently cooled to device operational temperature, typically room
temperature. As the thermal expansion coefficients of most silicides (e.g., thermal expansion
coefficients of solid-state reaction polycrystalline TiSi2, CoSi2, and NiSi are 12.5x10-6, 10.4 x106
, and 16 x10-6 K-1, respectively) are about five times larger than that of silicon (2.6 x10-6 K-1), a
tensile stress is induced in the silicide when cooled down.
59
oxide or nitride
metal
Si Substrate
PECVD Oxide
Anneal
Gap = 192.3 nm
Gap
silicide
(a)
500nm
Si Substrate
Silicide
Silicon Substrate
(b)
Fig. 3-5: (a) Process flow and (b) SEM cross-section of a 192nm air gap formed between oxide
and silicide. Here, 200nm-Mo reacts with silicon but not oxide at the anneal temperature.
a-Si or poly-Si
metal
Si Substrate
Silicide
PECVD Amorphous
Silicon
Anneal
silicide
silicide
Gap
Gap = 127.8 nm
Silicide
300 nm
Silicon Substrate
Si Substrate
Fig. 3-6: Process flow and SEM cross-section of a 128 nm air gap formed between amorphous
silicon and silicide. Here, 150 nm Mo forms silicides unevenly on both sides due to differences
in single-crystal and amorphous Si silicidation behavior and also likely due to presence of
hydrogen and oxygen in the amorphous Si.
3.3.2 Repeatability
The solid-state silicide reaction is sensitive to impurities at the metal-Si interface and in the
metal itself. Three precautions have been experimentally found useful for repeatable and high
quality silicide formation:
1. The interface between the metal and semiconductor must be clean and free from native
oxide. To ensure this, samples are dipped into 5:1 buffered hydrofluoric acid (BHF) prior
to metal sputtering.
2. Native oxide can further be removed by a slight in-situ sputter etch preceding the actual
60
metal sputtering step. Caution should be taken here, as an aggressive sputter etch may
make the silicon surface and the resulting silicide surface rougher.
3. To reduce the background concentration of water vapor in the process chamber, wafers
are baked at 200 °C for 20 minutes in vacuum to degas before metal sputtering. In this
work, Mo is sputtered at 200 °C, so no cool down is required after dehydration baking.
Caution should be taken when sputtering nickel. As dinickel silicide, Ni2Si, starts to form
at ~300 °C, elevated temperature in the substrate and high sputtering power can allow the
nickel to react with silicon immediately, which affects the resulting gap spacing after
silicidation annealing.
4. To minimize the impurities within the metal film, it is helpful to keep the base pressure of
the metal sputter tool below 1x10-7 Torr and run several dummy wafers to clean up the
metal target prior to processing device wafers.
5. Annealing must be performed with a low concentration of oxygen to ensure that the metal
does not oxidize during silicide formation. This is especially important for samples with
very thin metal (<10 nm) and anneal at high temperatures, as oxygen can quickly diffuse
through the thin metal and passivate the metal-silicon interface by forming silicon
dioxide, which prevents metal and silicon from reacting. The RTA tool in the Berkeley
Microlab is not equipped with a pump to remove the contamination from atmosphere
before flowing inert gases. A long purge of N2 in the RTA chamber is found to help
silicide formation.
The importance of obtaining a clean metal-silicon interface is immediately apparent when
oxide is present at the interface. In particular, when samples before metal deposition are shortly
dipped in piranha (H2SO4+H2O2) instead of BHF with no sputter etch, and the same thermal
annealing conditions applied, silicidation either does not happen or the silicide surface becomes
very rough, as shown in Fig. 3-7. The wavy surface can be explained by silicide protrusions
through areas with thinner oxide or without native oxide, causing nonuniform reaction between
the metal and the silicon.
Repeatable and uniform silicide-induced gaps can be formed with all of the above procedures
taken. Fig. 3-8 shows the fabrication process flow where an array of microchannels with various
dimensions is formed with one mask and only 1 minute of annealing to release. A blanket Mo is
sputtered followed by lithography and wet etching to pattern Mo (Fig. 3-8(a)). Then, PECVD
oxide is deposited on the entire wafer (Fig. 3-8(b)). RTA at 750 °C for 1 minute forms the
channel (Fig. 3-8(c)). As full 6‖ wafer RTA for this process is not possible in the Berkeley
Microlab, nine samples from the same 6‖ wafer (one from center, four from 4‖ area and four
from edges), were annealed and examined for uniformity and repeatability. Microchannels form
uniformly on die located at the same distance away from the center. The gap spacing is larger on
the center die as the Mo sputtering is not uniform, with thickest metal at the center. Fig. 3-9
shows five of the 15 um wide and 0.8 um high microchannels on one die with a zoomed-in view
on the insert that confirms the repeatability of this method.
61
3um
(a)
Oxide
Gap
200 nm
Silicide
(b)
Fig. 3-7: SEM cross-section showing a roughened silicide surface caused by thin oxide at the
silicon-metal interface.
Oxide
Metal
(a)
Si
(b)
Si
Silicide
(c)
Si
Fig. 3-8: Fabrication process flow of the microchannels in Fig. 3-9; (a) sputter blanket Mo films
on a single-crystal wafer and pattern via wet etch; (b) PECVD oxide; no pattern and etch is
required; (c) anneal to release the microchannels.
Capping Oxide
Channel Width = 15um
Channel Height
= 0.8um
Silicide
10um
Si Substrate
Fig. 3-9: Cross-sectional SEM of an array of oxide-capped micro-channels on a silicon substrate
fabricated via silicide-induced release.
62
3.3.3 Operational Temperature Range
To gauge the permissible temperature ceiling during process steps before and after the
silicidation anneal, samples of patterned Mo over Si were heated in a conventional oven at
350 ˚C for 6 hours before and after the 1 minute 750˚C silicidation anneal, with no change in
silicide step height, versus a sample without extra thermal treatments. This confirms that
microstructures can be released at the very end of a process as long as processing temperatures
after metal deposition do not exceed the silicidation temperature. Moreover, once the silicide is
formed, thermal processes with temperature much lower than the original silicidation
temperature generally do not change the size of the gap.
However, thermal treatments at temperatures higher than the initial silicide formation
temperature will affect the silicide morphology, of which the important consequence for silicideinduced gaps here is the surface roughness and the silicide step height change. The effects of
thermal treatment on silicide-induced gaps can be considered in two ways:
First, different silicide phases can form at higher temperatures and different phases have
different metal to silicon consumption ratio. For example, for Ni deposited on single crystal Si,
Ni reacts with Si at about 250 °C to form nickel-rich silicide, Ni2Si, with volume ratio of
consumed Ni:Si=1:0.91. When the temperature increases to around 350 °C, monosilicide, NiSi,
starts to form by consuming more Si and the volume ratio of consumed Ni:Si=1:1.84. The gap
spacing is expected to increase with more Ni2Si turning into NiSi. NiSi is stable on single crystal
Si until about 750 °C, at which point the high resistivity and silicon-rich phase, NiSi2, forms. As
temperature increases, the metal to silicon consumption ratio increases, as does the gap spacing.
Second, thermal treatments can change the silicide morphology via silicide agglomeration,
where the silicide agglomerates into discrete islands, as a result of a reduction of surface energy.
In the case of silicide formed with polysilicon, silicide-enhanced grain growth in the polysilicon
also increases the surface roughness. With even longer annealing time, silicide/poly-Si layer
inversion has been reported for both Ni and Co deposited on polycrystalline silicon [20][21]. The
onset of layer inversion can be detected by a sharp increase in resistance of the top thin film.
Both processes increase the surface roughness and resistance of the final silicide. The work in
[22] investigates how metal thickness (in particular, Co) relative to the polysilicon grain size
affects the degree of polysilicon grain growth, silicide agglomeration, and layer inversion.
In general, it is desirable to use silicide of a silicon-rich phase for better thermal stability.
Different approaches for improving the thermal stability of silicides have been reported,
including nitrogen implantation into the metal film before silicidation [23].
3.3.4 Small Gaps and Lateral Gaps
Among the most powerful capabilities provided by silicidation is its ability to achieve tiny
sub-50 nm gaps, which are essential to vibrating RF micromechanical resonators using
capacitive transduction. Fig. 3-10 shows a 32.5 nm gap underneath a SiGe capping layer,
achieved via a silicidation reaction between Mo metal and the underlying silicon substrate, with
comparatively little reaction with the capping SiGe layer. The thirty seconds required for
silicidation contrasts sharply with the 40+ minutes of wet-etching often required for smallgapped RF micromechanical resonators [15]. Indeed, release times required by etch-based
63
SiGe
Gap = 32.5 nm
200 nm
Silicide
Fig. 3-10: SEM cross-section of a 32.5nm gap formed between a bottom MoSi2 and a top SiGe
capping layer. Even smaller gaps should be achievable via a thinner metal layer.
release processes increase with gap aspect-ratio, while those needed for silicide-based release
remain virtually the same. Clearly, the described silicide-based release process scales much
better than etch-based counterparts. The smallest achievable gap is ultimately limited by the
surface roughness of the silicide which is generally on the order of 10 nm or less for nickel [24],
titanium [25], and cobalt [26] with proper thermal treatments. Gap spacings this small should be
very helpful towards capacitively transduced resonators with the sub-50 impedances desired
by conventional wireless circuits.
The silicide-induced release can also be applied to form lateral gaps, perhaps using PECVD
and/or atomic layer deposition (ALD) methods to deposit conformal lateral semiconductor and
metal films with well-controlled thicknesses at temperatures lower than the silicidation
temperature.
3.3.5 CMOS Compatibility
It should be noted that silicide-induced release is not limited to silicidation with single crystal
silicon, but also works with amorphous and polycrystalline systems, and with semiconductor
materials other than silicon, e.g., SiGe. For example, Fig. 3-11 presents a gap formed between a
top oxide capping layer and a 1.2 µm PECVD amorphous-silicon layer deposited at 300˚C. This
confirms that the described silicide-based release process can be applied to MEMS/NEMS built
atop CMOS or on substrates other than silicon, such as glass, as long as a thin layer of
semiconductor is available.
Another requirement for CMOS compatibility is that the process temperature and time cannot
64
exceed the thermal budget of the underlying transistors. In that case, Ni silicide can be used
instead of Mo and Ti silicides, as Ni starts to react with silicon at temperatures as low as ~250
°C. The work in [27] has successfully shown that 5.8 GHz microwave annealing can facilitate
low resistance NiPtSi silicide formation at reduced process temperature at 250 °C compared to
the 600 °C required if conventional RTA were used. Laser annealing, with only mili-second
anneal, has been demonstrated to form shallow silicide without degradation on the performance
of transistors [28]. Another possible approach is to use embedded micro-heaters, such as
polysilicon strips, to perform local anneal and release by applying electrical currents.
3.3.6 Released Microstructure
Mere patterning of the capping layer before the silicidation anneal yields suspended movable
structures with more general geometries. Fig. 3-13 presents SEM cross-sectional images of
multiple oxide diaphragms released via the described silicide approach, including a 100×100
µm2 membrane with a 260:1 lateral dimension-to-vertical gap aspect ratio and membranes with
smaller sizes formed by the same one minute thermal anneal step (Fig. 3-13 (c)-(d)).
The required anneal time is independent of the lateral dimension. Therefore, diaphragms of
even larger lateral dimensions can be released with the same anneal time. On the other hand, the
smaller the gap spacing, the less annealing time is required to fully silicide the metal film. As the
lateral dimension of the structure and the gap spacing continue to increase and decrease,
1um
1.2um amorphous Si
Si-Sub
Fig. 3-11: A silicide-induced gap formed over a 1.2 µm PECVD amorphous silicon film
deposited at 300 °C.
150˚C PECVD a-Si
Nickel Silicide
Gap = 37.16 nm
Fig. 3-12: A 37 nm silicide-induced gap formed using low temperature nickel silicide. The
deposition temperature of the capping layer is 150 °C.
65
100um
(a)
10um
Oxide
Silicide
3um
(c)
Gap
Gap = 384.7 nm
2um
(b)
(d)
1um
Silicide
Fig. 3-13: SEM cross-sections of (a) a 100m-wide 410nm-thick oxide diaphragm suspended
385nm above the substrate and (b) a zoom-in. The original Mo thickness was 400nm. (c) and (d):
Smaller diaphragms released in the same annealing step.
respectively, the aspect ratio increases from both factors with decreasing required annealing
time. From this perspective, the method of silicide-induced gaps for releasing microstructures
offers infinite achievable aspect ratio with minimum release time, on the order of one minute of
less, compared to hours or days required by sacrificial material etch for such high aspect ratio
microstructures.
Theoretically, as silicidation is a solid-state reaction without gaseous reaction byproducts, the
silicide-induced gaps are expected to have vacuum. If the cavity underneath the released
diaphragm is at vacuum state, the calculation shows that the force generated from pressure
difference above and below the diaphragms would push these ~400 nm diaphragms down to the
substrate. This behavior is, however, not observed in the inspections using both optical and
mechanical probing methods. As the oxide is deposited via low temperature plasma enhanced
CVD, the oxide film showed obvious pin holes. It is very possible that gas diffuses through the
thin diaphragms or the PECVD oxide outgases during annealing such that vacuum state is not
achieved. More careful selection of materials and dimensions of the capping/sealing layers is
expected to address this issue.
Fig. 3-14 and Fig. 3-15 present 20 µm long, 2 µm wide oxide cantilever and a folded-beam
comb-driven resonator with springs bent by a probe, confirming that they are released.
Successful release of such compliant microstructures is possible because silicidation is a dry
process, so does not suffer from stiction. In all cases, the release anneal takes no more than two
minutes, and no etchant is consumed, making this approach much faster and cheaper than etchbased release methods.
66
3um
Release Cantilever
Contour
Contour
Fig. 3-14: SEM of a 1.2m-thick oxide cantilever separated from the substrate by a silicideinduced gap.
Fig. 3-15: SEM of a released folded-beam comb-driven structure with springs bent by a probe
tip.
3.3.7 Released Titanium Beam Resonators
To demonstrate the use of silicide-induced gaps in a practical application, the three-mask
process shown in Fig. 3-16 uses titanium (Ti) as a structural material and Mo as the siliciding
metal to fabricate beam resonators. Here, Mo is sputter deposited after a short in-situ sputter etch
to remove native oxide, then patterned using a commercial aluminum wet etchant (pre-mixed
phosphoric and acetic acid mixture) at 50 ˚C. Next, 300nm of 300˚C PECVD oxide isolation
liner is deposited and patterned via a BHF dip, followed by sputter deposition of 700 nm of Ti
structural material at 300 ˚C. The Ti is then dry etched via a Cl2/BCl3 plasma, with the etch
stopping on the underlying Mo or oxide layer. The structure is finally released via a one minute
67
rapid thermal anneal step. As shown in Fig. 3-16, MoSi2 forms the ground plane/drive electrode
for this clamped-clamped beam, and the oxide layer prevents the beam from shorting with the
silicide.
Fig. 3-17 presents the SEM of a released 320 m long, 3 m wide Ti clamped-clamped beam
displaced laterally by a probe tip. Fig. 3-18 further presents the mixing-measured [15] frequency
characteristic (in vacuum) for a 20 m long, 2 m wide beam with 150 nm electrode-toresonator vertical gap spacing, confirming functionality of the beam and applicability of the
silicide-based release process in an actual application.
Mo
Oxide
Si
(a)
(b)
Oxide
Si
(c)
Si
Ti
Ti
Mo
Oxide
Mo
(d)
MoSi2
Si
Fig. 3-16: Process flow yielding a titanium clamped-clamped beam released via silicidation: (a)
Sputter and pattern molybdenum over silicon substrate; (b) deposit 300 nm thick 300 ˚C PECVD
oxide and remove over device areas and bond pads; (c) sputter and pattern 700 nm thick titanium
structural material; and (d) release via rapid thermal annealing at 750 ˚C.
Silicide
30um
Oxide
Titanium Beam
(a)
Probe tip
Contour
(b)
Fig. 3-17: (a) SEM of a 320 m long, 3 m wide, 700 nm thick titanium clamped-clamped beam
using the process of Fig. 3-16. (b) Bending via a probe tip confirming release.
68
Fig. 3-18: Mixing measurement setup and measured resonant peak under vacuum for a Ti
clamped-clamped beam released via silicidation, with Q = 1,082. Here, PRF = 10 dBm (network
analyzer output), VLO = 10 VP-P, and VP = 20 V.
3.4. Conclusions and Future Work
By utilizing a volume shrinkage-based method for forming gaps between structural layers
and thereby avoiding the need for etching, the silicide-based release process demonstrated in this
work is cheaper, cleaner, and faster than conventional etch-based methods, as it requires no
etching, consumes no chemicals, and has little dependence on mass transport processes. Using
this method, structures with aspect-ratios exceeding 260:1 have been released in less than two
minutes—substantially less than the 40 minutes otherwise required by an etch-based release
process. Although this work features silicides based on Mo, it should be understood that any of
the metals in Table 3-1 could also be used.
But the benefits of silicidation methods go far beyond mere release of high-aspect ratio gaps.
In particular, the fact that silicidation is a heat-induced and self-sufficient reaction that does not
require a diffusion path suggests the possibility for localized and post-package release without
any need for release holes in the package structure. To expand upon this, Fig. 3-19(a) [29]
presents one conventional approach to wafer-level encapsulation where release holes in the
encapsulating cap are needed to allow release etchants to access a sacrificial layer that
completely encases the structure under the cap. Since the diffusion paths are quite tortuous, the
time required for release is generally quite long and etch by-products have difficulty diffusing
out. On top of this, the need to seal the etch holes can compromise both the package and device
within (if the sealant also deposits on the device).
69
In contrast, silicidation (requiring no diffusion path) can form gaps submerged beneath the
cap layer with no need for etch holes, as shown in Fig. 3-19(b). The packaging process would
require just minutes of anneal time and would be local to areas with the right metalsemiconductor pairings. Efforts towards post-package and release of capacitive resonators are
ongoing.
Sacrificial Material
(a-1)
Structure
(b-1)
Permeable Material
Etch Holes
Si Sub.
(a-2)
“Sacrificial” Metal
Package
or Frame
Material
Si Sub.
Sealing Layer
Si Sub.
Released Structure
(b-2)
Silicide
Si Sub.
Fig. 3-19: Cross-sectional summaries of (a) a conventional thin-film package where (a-1) etch
holes provide access for sacrificial material removal and (a-2) a deposition step is required to
seal; and (b) a silicide-based release packaging method that obviates the need for etch holes and
sealing that comprises (b-1) deposition and patterning of a proper succession of semiconductors
and metals and (b-2) a short silicidation anneal.
3.5. References
[1] M. A. Schmidt, "Wafer-to-wafer bonding for microstructure formation," Proceedings of the
IEEE, vol. 86, pp. 1575-1585, 1998.
[2] D. Xu, L. Wang, G. Ding, Y. Zhou, A. Yu, B. Cai, ―Characteristics and fabrication of
NiTi/Si diaphragm micropump,‖ Sensors and Actuators, A93 (2001) 87-92.
[3] J. Chae, H. Kulah and K. Najafi ―A CMOS-compatible high aspect ratio silicon-on-glass inplane micro-accelerometer,‖ J. Micromech. Microeng. vol. 15. 2005, pp. 336-345.
[4] F. Niklaus, G. Stemme, J.-Q. Lu, and R. J. Gutmann, ―Adhesive wafer bonding,‖ J. OF
APPLIED PHYSICS, vol. 99, 031101, 2006.
70
[5] H.-S. Noh, K.-S. Moon, A. Cannon, P. J Hesketh and C P Wong, ―Wafer bonding using
microwave heating of parylene intermediate layers,‖ J. Micromech. Microeng. 14 (2004)
625–631.
[6] R. F. Wolffenbuttel and K. D. Wise, "Low-temperature silicon wafer-to-wafer bonding
using gold at eutectic temperature," Sensors and Actuators A: Physical, vol. 43, pp. 223-229,
1994.
[7] T. Suni, K. Henttinen, J. Dekker, H. Luoto, M. Kulawski, J. Makinen, R. Mutikainen,
―Bonded thick film SOI with pre-etched cavities,‖ Microsyst Technol (2006) 12: 406–412.
[8] W. C. Tang, T.-C. H. Nguyen, M. W. Judy, and R. T. Howe, "Electrostatic-comb drive of
lateral polysilicon resonators," Sensors and Actuators A: Physical, vol. 21, pp. 328-331,
1990.
[9] F. Marty, L. Rousseau, B. Saadany, B. Mercier, O. Français, Y. Mita, and T. Bourouina,
"Advanced etching of silicon based on deep reactive ion etching for silicon high aspect ratio
microstructures and three-dimensional micro- and nanostructures," J. of Microelectronics,
vol. 36, pp. 673-677, 2005.
[10] R. Abdolvand and F. Ayazi, "An advanced reactive ion etching process for very high aspectratio sub-micron wide trenches in silicon," Sensors and Actuators A: Physical, vol. 144, pp.
109-116, 2008.
[11] R. Maboudian and R. T. Howe, ―Critical review: Adhesion in surface micromechanical
structures,‖ J. Vacuum Sci. Technol., vol. B15, no. 1, pp. 1–20, Jan./Feb. 1997.
[12] C. Torres-Raya, D. Hernandez-Maldonado, J. Ramirez-Rico, C. Garcia-Gañan, A. R. de
Arellano-Lopez, and J. Martinez-Fernandez, ―Fabrication, chemical etching, and
compressive strength of porous biomimetic SiC for medical implants‖ J. Ma-ter. Res., vol.
23, no. 12, Dec 2008.
[13] I. Lee, G. H. Yoon, J. Park, S. Seok, K. Chun, and K.-I. Lee, "Development and analysis of
the vertical capacitive accelerometer," Sensors and Actuators A: Physical, vol. 119, pp. 818, 2005.
[14] K. R. Lee, K. Kim, H.-D. Park, Y. K. Kim, S.-W. Choi, and W.-B. Choi, ―Fabrication of
capacitive absolute pressure sensor using Si-Au eutectic bonding in SOI wafer,‖ J. Phys.:
Conf., ser. 34 393-398, 2006.
[15] J. Wang, Z. Ren, and C. T.-C. Nguyen, ―1.156-GHz self-aligned vibrating micromechanical
disk resonator,‖ IEEE Trans. Ultrason., Ferroe-lect., Freq. Contr., vol. 51, pp. 1607-1628,
Dec. 2004.
[16] W. H. Teh, C.-T. L., M. Graham, and C. G. Smith, "Cross-linked PMMA as a lowdimensional dielectric sacrificial layer," Microelectromechanical Systems, Journal of, vol.
12, pp. 641-648, 2003.
[17] A Bagolini, L Pakula, T LMScholtes, H TMPham, P J French and P M Sarro, ―Polyimide
sacrificial layer and novel materials for post-processing surface micromachining,‖ J.
Micromech. Microeng. 12 (2002) 385–389.
[18] K. Maex and M. Rossum, Properties of Metal Silicides, IN-SPEC Publication, 1995.
71
[19] L. J. Sung and C. Y. Lu, "Limitation of spacer thickness in titanium salicide ULSI CMOS
technology," Electron Device Letters, IEEE, vol. 10, pp. 481-483, 1989.
[20] E. G. Colgan, J. P. Gambino, and B. Cunningham, "Nickel silicide thermal stability on
polycrystalline and single crystalline silicon," Materials Chemistry and Physics, vol. 46, pp.
209-214, 1996.
[21] E. G. Colgan, J. P. Gambino, and Q. Z. Hong, "Formation and stability of silicides on
polycrystalline silicon," Materials Science and Engineering: R: Reports, vol. 16, pp. 43-96,
1996.
[22] J. P. Gambino, E. G. Colgan, A. G. Domenicucci, and B. Cunningham ―The Thermal
Stability of CoSi2 on Polycrystalline Silicon: The Effect of Silicon Grain Size and Metal
Thickness,‖ J. Electrochem. Soc., Vol. 145, No. 4, April 1998, pp. 1384-1389.
[23] S. Wein-Town, L. Ming-Chi, and C. C. H. Hsu, "Suppression of cobalt silicide
agglomeration using nitrogen (N2+) implantation," Electron Device Letters, IEEE, vol. 19,
pp. 163-166, 1998.
[24] M. Bhaskaran, S. Sriram, A. S. Holland, and P. J. Evans, "Characterisation of nickel silicide
thin films by spectroscopy and microscopy techniques," Micron, vol. 40, pp. 99-103, 2009.
[25] C. Lavoie, R. Martel, C. Cabral, Jr., L.A. Clevenger and J.M.E. Harper, ―Surface roughening
during titanium silicide formation: a comparison between Si(100) and poly-Si substrates,‖
Proceedings of MRS, vol. 440, pp. 389-394, 1997.
[26] G.-P. Ru, B.-Z. Li, G.-B. Jiang, X.-P. Qu, J. Liu, R. L. Van Meirhaeghe, and F. Cardon,
"Surface and interface morphology of CoSi2 films formed by multilayer solid-state
reaction," Materials Characterization, vol. 48, pp. 229-235, 2002.
[27] T. Yamaguchi, Y. Kawasaki, T. Yamashita, Y. Yamamoto, Y. Goto, J. Tsuchimoto, S.
Kudo, K. Maekawa, M. Fujisawa, and K. Asai, "Low-resistive and homogenous NiPtsilicide formation using ultra-low temperature annealing with microwave system for 22nmnode CMOS and beyond," in Electron Devices Meeting (IEDM), 2010 IEEE International,
pp. 26.1.1-26.1.4.
[28] C. Ortolland, E. Rosseel, N. Horiguchi, C. Kerner, S. Mertens, J. Kittl, E. Verleysen, H.
Bender, W. Vandervost, A. Lauwers, P. P. Absil, S. Biesemans, S. Muthukrishnan, S.
Srinivasan, A. J. Mayur, R. Schreutelkamp, and T. Hoffmann, "Silicide yield improvement
with NiPtSi formation by laser anneal for advanced low power platform CMOS
technology," in Electron Devices Meeting (IEDM), 2009 IEEE International, 2009, pp. 1-4.
[29] K. S. Lebouitz, A. Mazaheri, R. T. Howe, and A. P. Pisano, "Vacuum encapsulation of
resonant devices using permeable polysilicon," Technical Digest, 12th Int. IEEE Micro
Electro Mechanical Systems Conference (MEMS). 1999, pp. 470-475.
72
4. Capacitive-Piezoelectric Resonators
4.1 Raising Q of Piezoelectric Resonators
In pursuit of a solution for applications mandating low process temperature and high
linearity, this section focuses on enhancing Q of piezoelectric resonators to achieve simultaneous
high-Q and low impedance resonators. Plenty of researchers have recognized the adverse effects
of metal electrodes on Q and sought to raise the Q‘s of thin-film piezoelectric resonators, with
approaches that span from reducing electrode roughness [2], to optimizing the electrode material
[3], to carefully balancing the AlN-to-electrode thickness ratio [4], to use of a Bragg reflector to
prevent energy loss [5], none of the above methods raises the Q‘s of on-chip piezoelectric
resonators anywhere near the >10,000 values needed for RF channel-selection and frequency
gating spectrum analyzers.
Yet, polysilicon resonators easily achieve such Q values (but with higher than-desired
impedances). To date, the measured Q‘s of polysilicon resonators are on the order of 20 times
larger than that of sputtered AlN resonators at similar frequencies. Interestingly, material loss
theory [6][7][8] predicts that the (f•Q) product limit due to (dominant) phonon-phonon
interactions in the AlN material itself is less than two times lower than that of silicon, shown in
Table 1. While the measured Q of silicon (either poly-silicon (e.g., Q=161,000 at 61.9 MHz [9])
or single-crystal silicon (e.g., Q=77,000 at 85.9MHz [10])) resonators have approached the
theoretical value, Q‘s of AlN resonators demonstrated so far fall far behind the theoretical value.
Table 4-1: Material properties of doped silicon and aluminum nitride used for simulation of the
theoretical phonon-phonon-limited damping coefficient and the corresponding material Q at
1GHz.
Parameter
Doped Si
AlN
Unit
Density, ρ
2330
3230
Kgm-3
Specific Heat, CV
1.658x106
1.374x106
Jm-3K-1
Thermal Conductivity, K
130
285
Wm-1K-1
Velocity of Longitudinal Wave, VL
8387
10908
ms-1
Velocity of Shear Wave, VS
5830
5567
ms-1
Debye Velocity, VD
6337
6237
ms-1
Thermal Relaxation Time, τ
5.85x10-12
1.64x10-11
s
Gruson number
1.054
1.236
―
Damping Coefficient, αp-p
4.64 x10
Phonon-phonon limited material Q at 1 GHz
-17
50,745
73
4.86 x10
-17
37,609
m-1s-2
―
This large deviation is unlikely due to the difference between material properties of singlecrystal AlN used for simulation and sputtered AlN used in the experiments, given the fact that
the measured Q of a thickness-mode FBAR made of epitaxial single-crystal AlN deposited via
MOCVD (Metalorganic Chemical Vapor Deposition) on SiC wafer at extremely high
temperature (1200~1300°C) [11] is essentially the same Q, Q~1,000, as FBARs made of
sputtered AlN. The only data point of high-Q MOCVD epitaxial AlN resonator is 21,000
measured at cryogenic temperature of 4K for a 82.585-MHz clamp-clamp beam resonator via
magneto transduction [12], while Q at room temperature is unknown.
This suggests that the sputtered AlN material itself might not be the principal culprit among
Q-limiting losses, but rather the metal electrodes or the electrode-to-resonator interface strain
might be more responsible. In fact, experimental data shows that as the thickness of a
piezoelectric resonator‘s electrode increases, both the resonance frequency and Q of the
resonator drop due to mass loading and electrode loss, respectively [13]. Electrode-derived
energy loss perhaps also contributes to the lower Q‘s measured in d31-transduced AlN resonators,
where the electrodes often cover locations with the maximum strain, versus the Q‘s of d33transduced thickness-mode resonators, where electrodes are placed very close to the nodes of the
acoustic standing waves. Despite their lower Q‘s, d31-transduced resonators are arguably more
attractive than d33, since their frequencies are set by CAD-definable lateral dimensions, so are
more suitable for on-chip integration of multiple frequencies.
Whether a resonator uses d31 or d33, both share the common problem that Q degrades as
dimensions scale to achieve larger coupling and/or higher frequencies. In particular, while a
piezoelectric structure can be scaled, its electrode thickness often cannot scale as aggressively,
since doing so incurs excessive electrical loss derived from increased electrode and interconnect
electrical resistance. If a designer attempts to compensate for this by using thinner, but wider,
metal traces, then the beams supporting the resonator would need to be wider to accommodate
the wider metal traces, and wider beams incur more energy loss through supports and anchors,
hence lower Q. If the width of the support beams are decreased in order to reduce anchor losses
and raise Q, the width of the metal traces must also be decreased, which then increases their
resistance, again, lowering Q and negating the gains.
Admittedly, there are materials with higher predicted intrinsic material Q values, such as
diamond [14] and SiC, which may be better candidates to serve extremely-high-Q demands
(Q>100,000). However, those materials demand high temperature deposition steps and so are not
CMOS compatible. On the other hand, AlN can be deposited at room temperature via reactive
sputtering of a pure aluminum target in nitrogen. The measured Q‘s of low-temperature
resonators capable of being built directly on CMOS with process temperature less than 400°C
(i.e. without using silicon substrate as the resonator structure layer), either use purely back-end
metal ([16], IBM process), ([17], AMS process), back-end metal and dielectric composite ([18],
TSMC process) [19], sputtered titanium [20], AlSi 1% [21], or electroplated nickel resonators
[22], are lower than 2,000, except for the work of disk and ring resonators made of electroplated
Ni by Huang, et. al. [23][24]. Inspired by the theoretical prediction of Q values in Table 4-1, if
there is a way to eliminate the adverse effects of metal electrodes, AlN is likely to provide a high
Q and simultaneously low-impedance solution for low-temperature, CMOS-integration
applications. The significance of eliminating electrode-associated losses to restore Q of thin-film
piezoelectric resonators made of sputtered AlN thus transcends scientific interest and may offer
practical value.
74
Vibration Mode Shape
y
Input Electrode
Output Electrode
x
vi
AlN
z
AlN
x
(a)
(1) Reverse Piezoelectric Effect
(2) Piezoelectric Effect
…
Thicker Electrode
iout
d1
vi
t
d3
EAlN
SP
SP
DP
Thicker Electrode
(3) Induced Charges on Electrodes
(b)
Fig. 4-1: (a) Conventional piezoelectric transducers employing electrodes that directly contact
the piezoelectric structure (i.e. AlN film); and (b) working principal of a capacitive-piezo
resonator for which electrodes are separated from the piezoelectric structure via small air gaps.
4.2 Capacitive-Piezoelectric Transducers
From the above discussion, it seems that Q degradation cannot be avoided as long as the
electrode is in physical contact with the piezoelectric structure (which generates loss through
strain coupling) and as long as the piezoelectric structure governs the size and thickness of the
electrode (which governs electrical loss). To minimize the energy loss associated with electrodes
and the resonator-electrode interfacial defects, researchers have used undoped AlGaAs for a
piezoelectric resonator and doped AlGaAs with Si (AlGaAs:Si) for its electrodes to replace
metals conventionally used in piezoelectric resonators, all of which are single-crystal deposited
via MOCVD at 580°C, and have demonstrated Q of 25,390 at 21.77 MHz [25]. However, the
process temperature is too high for on-chip integration. Interestingly, instead of using high-Q
materials for the electrodes, all of these issues can be circumvented by mechanically decoupling
75
iL
Cg
vin
Cp
AlN
ip
Cp
vin
Cp
Cp
Cg
Cg
(a)
Cg 1:ηDrive lm cm rm ηSense:1 Cg
Cg RL
Cg
(b)
(c)
RL
Cg
Fig. 4-2: Equivalent electrical circuit at (a) input and (b) output, modeling the effect of gap
spacing on the electromechanical coupling coefficient; (c) equivalent circuit of a capacitivepiezo resonator.
the electrodes from the resonating body via separation of the electrodes from the vibrating
structure so that they are no longer in contact, as shown in Fig. 4-1(b).
The working principal of the resulting transducer, dubbed the ―capacitive-piezo‖ transducer,
is similar to a conventional piezoelectric resonator: (1) on the input, voltage applied across two
electrodes generates an electric field across the piezoelectric resonator, which induces
mechanical strain via the reverse-piezoelectric effect; (2) on the output, the mechanical strain
induces electrical displacement current Dz via the piezoelectric effect; (3) the equivalent bonded
surface charge further induces charges of opposite sign on the electrodes separated by a gap.
The capacitive-piezo transducer should not only raise the Q of the piezoelectric film, but
should also allow much thicker (and thus much less resistive) electrodes without the electrode
loss and mass loading penalties that would otherwise result if the electrode is contacted as in Fig.
4-1(a). Thicker electrodes should also further increase the Q, since the electrode parasitic series
resistance would be smaller.
Although not a well known technique, the use of contactless electrodes on piezoelectric
resonators is actually not new. This strategy had in fact been demonstrated on 5- and 10-MHz
quartz crystal resonators, called BVA resonators, as far back as 1977 [26]. Since the
piezoelectric-to-electrode thickness ratio of these devices was on the order of 100μm-to-100nm,
or 1000, separating the electrode from the piezoelectric did little to increase the Q of the device.
It did, however, allow for a more stable device against drift, since it eliminates electrode-toresonator stress variations over time [27]. This was the main reason for investigating such
devices in the past.
For micromechanical resonators, on the other hand, the piezo-electric-to-electrode thickness
ratio is much smaller, on the order of 10. Thus, the case for using a ―capacitive-piezo‖ transducer
is much stronger on the micro-scale. In addition, the ease with which small electrode-toresonator gaps can be achieved via MEMS technologies further encourages the use of contactless
electrodes. In effect, capacitive-piezo transducers stand to improve the Q and drift stability of
micro-scale thin-film piezoelectric resonators with very little increase in fabrication cost.
76
4.3 Analytical Modeling
4.3.1 Electromechanical Coupling Coefficients
Electrical models for AlN contour-mode resonators with contacting electrodes are discussed
in Chapter 1 and will not be repeated here. The present approach to modeling the capacitivepiezo resonator focuses on how electrode-to-resonator air gaps influence the electrical model
parameters, specifically, the electromechanical coupling coefficients, ηDrive and ηSense in Fig. 2(c),
defined as
Drive 
F ( j )
Vin ( j )
(4-1)
at the input (or ‗driving‘ port), where F(jω) is the generated modal force and Vin(jω) is the input
voltage across the top and bottom electrodes. Sinusoidal input is assumed through the entire
analysis. ηDrive models how efficiently the energy in the electrical domain as a voltage input can
be transduced into mechanical domain as a force driving the resonator to vibration, and

Dz dA
QP ( j ) A
Sense 

U ( j ) U ( j )
(4-2)
at the output (or ‗sensing‘ port), where QP is the total charge induced via the piezoelectric effect
and equals the displacement current (charge/area), Dz, integrated over the electrode area; U(jω) is
the value of the maximum displacement. ηSense models how efficiently the energy in the
mechanical domain as displacement can be transduced into electrical domain as a current output.
When the input signal is applied across the top and bottom electrodes, mechanical strain, Sr,
is induced on the AlN film via the reverse piezoelectric effect. The induced strain equals the
product of the piezoelectric stress constant, e31 (e31~0.7 C/m2 for sputtered AlN), and the electric
field established within the AlN film, EAlN. The gap-AlN-gap stack can be modeled by three
capacitors in series, as shown in Fig. 2(a), from which EAlN can be written as
E AlN 
vin
H   z dTotal

vin
   E AlN,dTotal0  
H
(4-3)
where εz (~9) and H are the relative permittivity in the c-axis direction and thickness of AlN,
respectively; dTotal is the total gap spacing (dTotal=d1+d3); α is a function gauging how much the
coupling coefficient degrades with increasing air gap spacing:

H
H   z dTotal
(4-4)
(4-4) shows that α is no larger than unity and α = 1with no air gaps, i.e., dTotal = 0.
Fig. 4-4(a) plots α against gap spacing d on both sides for different piezoelectric materials with
1.5 µm thick piezoelectric resonator structure. To maximize EAlN given a fixed input voltage, α
must be maximized by utilizing small gaps and piezoelectric materials with low permittivity.
77
Input
Electrode
Output
Electrode
Ri
Rie
Input
Electrode
Ri
Ro
Roe
Gap Spacing d
(a)
AlN Ring Thickness = H
(b)
Poly-Si Ring Thickness = H
Fig. 4-3 : Electrode arrangement of (a) capacitive-piezo AlN ring resonator and (b) capacitive
poly-Si ring resonator for the same mode shape with resonance frequency at 1.2 GHz.
When the input frequency matches the resonance frequency, the lateral force associated with
the induced strain Sr excites the resonator into lateral-mode vibration, with the interested mode
shape shown in Fig. 4-1. Note that for this particular mode shape, there is ideally no strain,
stress, or displacement associated with the angular component. The generated modal force can be
written as the product of the induced stress, Tr, the cross-sectional area normal to the stress,
(rdrdθ), and the normalized mode shape, Ф(r,θ), together integrated over the electrode coverage
area:
F 
2
0

Roe
Rie
Tr ( Hrdrd )( r, )  (Tr H )  
2
0

Roe
r( r, )drd
(4-5)
Rie
where Rie, and Roe are the inner and outer radius of the electrode, respectively, as indicated in
Fig. 4-3(a). The distributed stress Tr is
V

Tr  EP Sr  e31Ez  e31 in   
H

(4-6)
where EP is the Young‘s modulus. The normalized mode shape is
 ( r,  ) 
 ( r,  )

Ro
 ( r,  )dr
(4-7)
Ri
where υ(r) is the mode shape normalized to the maximum value (i.e. υ(r)<=1 for any r in the
domain and υ(r)=1 at the largest displacement point). For a ring vibrating in the lateral direction,
υ(r) can be expressed as
 ( r,  )   r ( r )er   ( r )e
(4-8)
where
dY (hr)
n
n
 dJ n (hr)

B n
 C J n (kr )  D Yn (kr )  cos(n )
dr
dr
r
r


 r ( r,  )   A
 n
 r
n
r
  ( r, )    A J n (kr)  B Yn (kr )  C
dJ n (hr)
dY (hr) 
D n
  sin( n )
dr
dr

78
(4-9)
(4-10)
where Jn(x) and Yn(x) are the Bessel functions of the first kind and the second kind, respectively,
and h and k are functions of resonant frequency defined as:
h  o
k  o

(4-11)
E P (1   2 )

(4-12)
2 E P (1   )
where ωo is the resonant angular frequency and ρ, σ, EP are the AlN density, Poisson ratio, and
Young‘s modulus, respectively.
The four unknown constants, A, B, C, D, can be obtained by applying the traction-free boundary
conditions at the inner and outer radius of the ring
Trr |r  ri  0,
Trr |r  ro  0,
Tr |r  ri  0,
Tr |r  ro  0
(4-13)
Eq. (4-13) represents four equations which can be written in a 4x4 matrix form
 M 11
M
 21
 M 31

 M 41
M 12
M 22
M 32
M 42
M 13
M 23
M 33
M 43
M 14   A  0
M 24   B  0
  
M 34   C  0
   
M 44   D  0
(4-14)
where
M 11  n(n  1) J (n, hri )  0.5k 2 ri 2 J (n, hri )  hri J ( n  1, hri )
(4-15-1)
M 12  n(n  1)Y (n, hri )  0.5k 2 ri 2Y (n, hri )  hriY (n  1, hri )
(4-15-2)
M 13  n( n  1) J ( n, kri )  nkri J ( n  1, kri )
(4-15-3)
M 14  n ( n  1)Y ( n, kri )  nkriY ( n  1, kri )
(4-15-4)
M 21  n(n  1) J (n, hro )  0.5k 2 ro2 J (n, hro )  hro J (n  1, hro )
(4-15-5)
M 22  n(n  1)Y (n, hro )  0.5k 2 ro2Y (n, hro )  hroY (n  1, hro )
(4-15-6)
M 23  n( n  1) J ( n, kro )  nkro J ( n  1, kro )
(4-15-7)
M 24  n( n  1)Y ( n, kro )  nkroY ( n  1, kro )
(4-15-8)
M 31  n( n  1) J ( n, hri )  nhri J ( n  1, hri )
(4-15-9)
M 32  n ( n  1)Y ( n, hri )  nhriY ( n  1, hri )
(4-15-10)
M 33  n(n  1) J (n, kri )  0.5h 2 ri 2 J (n, kri )  kri J (n  1, kri )
(4-15-11)
M 34  n(n  1)Y (n, kri )  0.5h 2 ri 2Y (n, kri )  kriY (n  1, kri )
(4-15-12)
79
M 41  n ( n  1) J ( n, hro )  nhro J ( n  1, hro )
(4-15-13)
M 42  n ( n  1)Y ( n, hro )  nhroY ( n  1, hro )
(4-15-14)
M 43  n(n  1) J (n, kro )  0.5h 2 ro2 J (n, kro )  kro J (n  1, kro )
(4-15-15)
M 44  n(n  1)Y (n, kro )  0.5h 2 ro2Y (n, kro )  kroY (n  1, kro )
(4-15-16)
For a ring vibrating at the 2nd contour mode (anti-symmetric mode), n=0 in (4-9) and (4-10),
such that all terms related to the tangential direction, θ, become zero (i.e. the displacement is
independent of θ). The following analysis focuses on this particular mode shape.
The modal force F and ηDrive can therefore be found by plugging (4-7) and (4-6) into (4-5)
and further into (4-1):
F    e31  vin  2  r( r )dr
(4-16)
Drive    e31  2  r( r )dr
(4-17)
Roe
Rie
Roe
Rie
(4-17) indicates two interesting facts. First, ηDrive is proportional to both e31 and α, which is a
function of the permittivity εz. The optimized piezoelectric materials require high e31 and low
permittivity at the same time to achieve high electromechanical coupling coefficient. This is a
distinct feature of capacitive-piezoelectric versus piezoelectric transducers. Fig. 4-4(a) plots the
(e31 • α) product against total gap spacing, dTotal, for different piezoelectric materials. In general,
small gap spacing is preferred to maintain a high coupling coefficient. It should be noted that a
large e31 does not guarantee a large coupling coefficient. As shown in Fig. 4-4(b), even though
PZT has a larger e31 than AlN and ZnO, its capacitive-piezo coupling is weaker at most gap
spacings due to its much higher relative permittivity.
The electrode configuration affects ηDrive via the last term in (4-17). Given the same electrode
area and the static capacitance, coupling coefficient ηDrive is maximized by placing electrodes on
large displacement areas. This however degrades Q with larger energy dissipation due to larger
strain at the electrode/resonator interface and larger strain coupled to the electrodes.
On the sense side, vibration-induced strain polarizes the AlN film via the piezoelectric effect,
and the resulting electric displacement (charge per area) can be expressed as (with displacement
only in the radius direction)
 u u 
Dz  e31S r ,Sense  e31  r  r 
r
 r
(4-18)
where ur(r,jω) is the time-varying mechanical displacements in the radius direction as a function
of position r and can be decomposed into the product of a time-varying function U(jω) and the
stationary mode shape
ur ( r , j )  U ( j ) ( r )
80
(4-19)
1
0.8
H

H  2 z d
α
0.6
0.4
0.2
0
0
50
100
150
200
250
Gap Spacing (d1=d3=d) (nm)
e31 ·γ(d) (C/m2)
1
300
AlN
(e31=0.7 C/m2, εr=9)
ZnO
(e31=0.58 C/m2, εr=10)
PZT
(e31=7.2 C/m2, εr=1000)
0.8
0.6
0.4
0.2
0
0
100
200
300
Fig. 4-4: (a) Plot of α versus gap spacing (on each side) according to (4-4). The induced
electrical field within AlN film decreases by a factor of α with air gaps between the electrodes
and the resonator structure. The equivalent electromechanical coupling coefficients and static
capacitance on both input and output ports are all linear functions of α, therefore functions of gap
spacing. (b) The effective e31 on the drive side decreases as the gap spacing increases. The gap
spacing affects the coupling of PZT the most due to its much larger relative permittivity εr.
81
Integration of Dz over the electrode area gives the total induced charge, QP
QP 
2
Roe
0
Rie
  D rdrd
z
  ( r )

 2e31U ( j )  r
  ( r ) dr
r

Rie
ηSense can therefore be found by plugging (4-20 into (4-2):
Roe
(4-20)

  ( r )

  ( r ) dr
r

Rie
Roe
Sense  2e31   r
(4-21)
The time derivative of QP becomes the output current ip. The piezoelectric effect on the sense
side can thus be modeled by a current source with magnitude ip=ω•QP as shown in Fig. 4-2(b),
and the output current, i.e., the current flowing though RL (RL =50 Ω for measurement with a
network analyzer), becomes
iO  iP 
ZP
t
 iP 
 iP  
Z P  Z g  Z g  RL
t   r (d1  d 2 )
(4-22)
The parameter α can be absorbed into ηDrive to give a symmetric circuit shown in Fig. 4-2(c):
  ( r )

(4-23)
  ( r ) dr
r

Rie
ηSense,eq, the same as ηDrive, is proportional to e31 and α. The impedance of the resonator can
therefore be calculated according to
Roe
Sens,eq    e31  2   r
Rx 
rm
Sense Drive
(4-24)
where rm is the mechanical damping and is defined as
rm 
o mr
Q

olm
Q
(4-25)
where ωo is the resonant angular frequency, mr the effective mass, with value equivalent to lm in
Fig. 4-2(c).
Even though the coupling coefficients are each reduced by a factor of α compared to those of
contacting electrodes from (4-17) and (4-23), the impedance is not necessary lager. In fact,
according to (4-24) and (4-25), it is possible to obtain lower impedance with capacitive-piezo
transducers via lower mechanical damping rm with enhanced Q, if the increase in Q is larger than
α2.
From (4-17) and (4-23), neither of the electromechanical coupling coefficients is a function
of resonator thickness. In fact, thinner AlN structures offer the benefit of lower impedance due to
a reduction of effective mass mr and therefore the damping rm according to (4-24) and (4-25).
This is a distinct feature of capacitive-piezo lateral-mode resonators compared to capacitive
82
Piezoelectric
CP,1
ηDriveηSense /mrCP (s-2)
AlN
Capacitive-Piezo.
d
AlN
VP=30V
CP,2
Capacitive
VP=15V
Elec. d Poly-Si
VP=5V
CP,3
Fig. 4-5: Comparison of filter FOM of capacitive with VP of 5 V to 30 V, piezoelectric, and
capacitive-piezo transducers as a function of gap spacing, given the same filter bandwidth and
type. Capacitive-piezo transducers equipped with small gaps maintain high filter FOM as
piezoelectric ones, both filter FOMs are orders of magnitude higher than the case of capacitive
transducers. At VP=30 V, capacitive transducer has larger filter FOM when the gap is scaled
below 20 nm.
ones, where in the latter the coupling coefficients are proportional to the resonator thickness such
that a thinner resonator structure increases the impedance linearly. The benefit of scaling
piezoelectric resonator thickness emphasizes the need for separating electrodes as the electrodeto-resonator volume increases with a thinner resonator.
Moreover, both ηSense and ηDrive are functions of the gap spacing through α. Although air gaps
degrade effective coupling efficiency k2eff by a factor of α2, the higher Q provided by noncontacting electrodes together with sufficiently small gap spacings actually make it possible to
achieve higher Q• k2eff than piezoelectric resonators with contacting electrodes.
Perhaps the best way to compare different transducers is via the filter FOM previously
defined in Chapter 2 (2-7), repeated here
FOM 
1
 
 Drive Sense
RQ Co
mr Co
(4-26)
where RQ is the filter termination resistor, Co the static input capacitance, and mr the motional
mass of a constituent resonator in the filter. The right most form delineates parameters in the
expanded equation most relevant to resonator design.
Fig. 5 compares simulated plots of (ηDriveηSense,eq/mrCo) in the filter FOM for three different
transducers (i.e. piezoelectric, capacitive-piezo, and capacitive alone) versus gap spacing d at the
same frequency. The simulation uses a ring inner radius and thickness of 25.6 μm and 1.5 μm,
83
respectively; and ring widths of 5 μm for AlN and 4.3 μm for polysilicon, both chosen to achieve
a 1.2-GHz resonance frequency for both materials under the same mode shape, neglecting DC
bias-induced electrical spring softening inherent to capacitive resonators. In addition, the
electrodes for the polysilicon resonator are assumed to be placed both inside and outside the ring,
similar to [1] and plotted in Fig. 3(b). As expected, the FOM of the capacitive-piezo transducer
depends on gap spacing, but not as strongly as one might think, mainly because Co drops by the
same ratio α as the electromechanical coupling coefficient when the gap spacing increases. Even
so, a capacitive-piezo transducer with a 200 nm gap spacing achieves a filter FOM of 2.7x1017 s2
, for which a capacitive (alone) transducer with dc bias of 15V (VP=15V) would require a much
smaller gap spacing of 23 nm. This relaxed gap spacing is a distinct advantage of capacitivepiezo transducers over capacitive ones. At VP=30V, the capacitive transducer has a larger filter
FOM when the gap is scaled below 20 nm.
4.3.2 Frequency Shift and k2eff
This section focuses on a pure circuit method to investigate how gap spacing affects the
resonant frequency and the electromechanical coupling coefficients, reaching the same result as
the mechanical analysis in the previous section. Fig. 4-6(a) shows a typical BVD model for a
resonator with two capacitors, Cg1 and Cg2, representing capacitance contributed by air-gaps in
series to input/output ports and a parasitic capacitance Cp shunting to the ground. Cg1 and Cg2 can
be absorbed into the resonator branches to form an equivalent BVD model, shown in Fig. 4-6(b),
with modified component values
 C  Co 

L  Lx   g
 C

g


2
'
x


Cg2

Cx'  Cx  
 (C  C )(C  C  C ) 
g
o
g
o
x


(4-27)
(4-28)
2
 C  Co 

R  Rx   g
 C

g


where Cg is the total capacitance contributed by the air gaps on both sides:
'
x
Cg 
C g1  C g 2
C g1  C g 2
(4-29)
(4-30)
The last term in (4-29) is essentially α-2, which says that the addition of air gaps increases the
impedance by α-2. This is the same result as (4-17) and (4-23), where the equivalent
electromechanical coupling coefficients on both the input and output each contributes a
degradation ratio of α.
The series resonant frequency of Fig. 4-6(b) is
84
L’m C’m R’m
Lm Cm Rm
Cg
(a)
Cg
C’p
(b)
Cp
Fig. 4-6: Plot of a circuit method to show how air gaps affect both series and parallel resonance
frequencies and equivalent coupling coefficient. (a) a BVD model with two series capacitors, Cg1
and Cg2, representing air gaps on both input and output of the resonator; (b) equivalent BVD
model by absorbing Cg1 and Cg2 into the resonator branches.
f s' 
1
2
1
1
1

'
L Cx
2
'
x
Cx
Co  C g
Lx C x
 fs  1 
Cx
Co  C g
(4-31)
The series resonant frequency increases with the addition of air gaps. This upward frequency
shift comes from frequency-dependent impedance change on the signal path in the electrical
domain and should be considered separately from the frequency shift due to elimination of
electrode mass loading, which modifies the equivalent mass and stiffness of the resonator in the
mechanical domain. In fact, connecting a variable capacitor with a mechanical resonator is a
well-known technique to tune the mechanical resonator frequency [28].
When considering parallel resonance frequency, air-gap capacitor Cg is essentially in series
with the parasitic capacitance Cp, which originates mostly from interconnects and bonding pads.
1
1
f p' 
2
Cx
C gC p
Co 
Cg  C p
(4-32)
Lx C x
The parallel resonant frequency decreases with air gaps compared to that of a resonator with
contacting electrodes (i.e. Cp becomes infinity in (4-32)),
The effective electromechanical coupling coefficient, k’2eff, can be calculated by plugging (431) and (4-32) into
'
'
 2 f p  fs
k 

4
f p'
'2
eff
(4-33)
and rearranging into
k eff' 2  k eff2 
Cg

Cg

Co  C p
C g  Co C g  C p Co  C g C p /(C g  C p )
(4-34)
where k2eff is the effective electromechanical coupling coefficient without gap spacing (i.e. with
Cg approaching infinity). When the parasitic capacitance CP is minimized such that CP << Cg, the
85
d
H
d
(a)
Top Electrode
Top Electrode
d+2σx
x
(In Resonance)
(In Resonance)
H-2σx
d+2σx
d
Bottom
Bottom Electrode
Bottom
Bottom Electrode
(a)Electrode
(b)
(b)Electrode
Top Electrode
Top Electrode
d
(Static)
(Static) x
H
d+2σx
H-2σx
d+2σx
Fig. 4-7: Cross-section of a capacitive-piezo resonator (a) before deformation and (b) after
deformation, showing how gap spacing is modulated by lateral vibration amplitude x during the
Poisson ratio σ.
last two terms in (4-34) become unity. Therefore,
k eff' 2  k eff2 
Cg
C g  Co
 k eff2 ,o  
(4-35)
The result in (4-35) is not surprising because both the FOM described in (4-26) and k2eff defined
in (4-33) gauge the ‗bandwidth‘ of a micromechanical resonator, though their absolute values are
not the same.
Admittedly, capacitive-piezo transducers trade effective electromechanical coefficient for
higher Q. The good news is that the trade is not a one-to-one ratio. Specifically, the theoretical
prediction posts the Q ceiling of a AlN resonator to be ten to twenty times higher than the current
measurement data, while α is 0.45 for gap size of 100 nm and can be increased to 0.625 for 50
nm, as shown in Fig. 4(a). Note that losses associated with electrodes can be eliminated as long
as the strain is not coupled to the electrodes, regardless the gap size. Therefore, capacitive-piezo
transducers are likely to give the higher (k2eff · Q) product.
(4-34) also indicates that for capacitive-piezo transducers, it is important to minimize
parasitic capacitance to ensure the condition CP<<Cg holds such that k’2eff differs from k2eff only
by a factor α.
4.3.3 Linearity (PIIP3)
The addition of air gaps introduces a more dominating nonlinearity factor into the
transduction process than the nonlinearity of AlN material identified as the main contribution of
nonlinearity in other piezoelectric resonators without air gaps. The following analysis estimates
the degree of nonlinearity introduced by the air gaps. As the resonator is vibrating in the lateral
mode, the gap spacing is modulated by the lateral mechanical displacement, x, via the Poisson
ratio σ, as shown in Fig. 4-7. The total induced force with gap spacing modulation is obtained by
modifying α in (4-16):
FTotal  vin   
( H  2x )
( H  2x )  2 r ( d  x )
(4-36)
where σ is the Poisson ratio; to simplify the expression, parameters independent of x have been
lumped into one parameter β defined as
  2e31  r( r )dr
Roe
Rie
86
(4-37)
Here, a time-varying, position-independent lateral mechanical displacement amplitude, x(jω) is
used instead of ur(r,jω) defined in (4-19) to simplify the equation. Using Taylor expansion, (436) becomes
FTotal
  2 x ( j )  1  2 x ( j )  2

r
r
  
    
 vin ( j )      1  
  H  2 r d  2  H  2 r d 

(4-38)
The first term is the fundamental response; the second and the third terms are the sources of
intermodulation forces, FIM2 and FIM3, respectively, when the input signal contains interferences
at frequencies spaced equally from each other and from the center frequency of the resonator.
Specifically, when the input signal is
vin  vo  cos(1t  1 )  vo  cos(2 t  2 )
(4-39)
1  2 ( f o  f ) ; 2  2 ( f o  2 f )
(4-40)
where
where fo is the resonance frequency and Δf is the frequency difference. The mechanical
displacement x also contains terms at both frequencies ω1 and ω2
x  X 1  cos(1t  1 )  X 2  cos(2t  2 )
(4-41)
The amplitude X1 and X2 are related to the input signal via
X 1, 2 ( j ) 
F
1
H
 ( )  vin    
 1, 2
kre
kre H  2 r d
(4-42)
where Θ1 and Θ2 are the biquad systems transfer functions of two interferer signals, defined as
   2  j 
1, 2 ( j )  1   1, 2    1, 2 
  o   Q  o 
1
(4-43)
The 3rd-order intermodulation force FIM3 can be found by plugging (4-41) and (4-39) into the
third term of (4-38) and selecting the terms with frequency component equaling to fo
2
FIM 3


2 r
  
 (vo )  
 k re ( H  2 r d ) 
3
(4-44)
where
1
2
1
4


   1 2  12   cos(21t  2 t  21  2 )
(4-45)
To compare the linearity performance of capacitive-piezo versus capacitive transducers, it is
useful to compare PIIP3 value. At this extrapolated input power, the 3rd intermodulation
component of the total generated force in a two-tone test has the same value as the linear force
component. The required input voltage amplitude, VIIP3, can be found by equating FIM3 in (4-44)
to F in (4-16) and solve for vo:
87
VIIP 3
k ( H  2 r d )  1
1 
 re
  12  12 
2 Drive r
4 
2
1
2
(4-46)
As expected, the expression of VIIP3 only contains the electromechanical coupling coefficient on
the drive side, regardless of how the output signals are sensed on the sense side. PIIP3 can then be
written as
 VIIP2 3 

(4-47)
PIIP 3 (dBm)  10  log10 
1000

R
x 

Fig. 4-8 compares PIIP3 of AlN and poly-Si ring resonators with the same dimensions as
those considered earlier for FOM comparison. Here, Q=3,073 are assumed for both resonators
and VP=25V for the capacitive resonator. PIIP3 (in dBm) of capacitive-piezo resonators degrades
with decreasing gap spacing by (H+2εzd)2, while PIIP3 of capacitive resonator, according to the
equations derived in [29], is affected by the gap spacing up to 7th power, which is responsible for
the lower PIIP3 value and a sudden drop once the gap spacing is scaled down to 50nm or less. At
VP=25 V and d=18 nm, both resonators give Rx~80 Ω but the capacitive-piezo resonator offers
39dB higher PIIP3 than the capacitive resonator. It should be noted that capacitive-piezo
resonators utilize the high coupling nature of piezoelectric resonators to eliminate the need for
deep-submicron gap spacing as required by capacitive resonators to obtain low impedance. The
relaxed gap spacing facilitates fabrication and linearity requirement.
PIIP3 (dBm)
Moreover, the fact that AlN is a dielectric material with large dielectric strength (100
MV/µm) and that no DC voltage is required for normal operation spares capacitive-piezo
resonators the catastrophic failure mechanism inherent to capacitive resonators, whereby DC bias
across the electrode and conductive resonator structure generates large current when they touch
each other upon application of large driving force and permanently fuses the resonator and the
Fig. 4-8: Simulated PIIP3 (in dBm) of capacitive and capacitive-piezo transducers versus gap
spacing d on each side. The latter has much larger PIIP3 given the same gap spacing.
88
electrodes. Overall, addition of small air gaps to the traditional piezoelectric resonators offers
benefits of higher Q and possibly better long-term stability without suffering from linearity or
catastrophic failure as encountered by capacitive resonators.
4.4. Fabrication Process
4.4.1 Overall Fabrication Flow
AlN resonators employing capacitive-piezo transducers were fabricated using a newlydeveloped 6-mask low-temperature CMOS-compatible process summarized in Fig. 4-9. This
section walks through the fabrication flow step-by-step and the following sections provide more
details on some critical steps. Here, 250 nm oxide and 200 nm nitride as isolation layers are first
deposited on 6" high-resistance wafers, followed by lift-off of 30 nm aluminum and 60 nm
nickel, both deposited by evaporation, as interconnections and bottom electrodes (step #1). This
Ni layer will later serve first as an etch stop for patterning the structural layer and second as a
seed layer for electroplating the Ni anchor. The lift-off process uses two photoresist layers (I-line
resist on LOR3A) to realize fine Ni/Al features with smooth edges critical to AlN quality, as
shown in Fig. 4-12(b). The relatively thin bottom electrodes and interconnects here is a
compromised design to ensure good sputtered AlN quality and thin sacrificial molybdenum step
coverage in the following steps. A planarization step incorporated into the fabrication will allow
for thicker bottom electrodes and interconnects and further reduce the parasitic resistance.
To fully take advantage of capacitive-piezo transducers, 250nm molybdenum is then
sputtered at 200 °C to serve as the sacrificial layer. Sputtered molybdenum is used instead of
more common sacrificial materials such as oxide, silicon, or germanium to attain better c-axis
orientation of the sputtered AlN film. Next, molybdenum is patterned into patches covering each
individual device to further improve AlN quality (step #2 in Fig. 4-9). Reactive puttering of AlN
directly on molybdenum renders films of very high tensile stress (>500MPa). After patterning
molybdenum into patches with only ~5um distance between each molybdenum patch (i.e.,
molybdenum still covers ~99% of the entire wafer area), AlN can be sputtered on molybdenum
with low stress (< ±50MPa) and high FWHM (~1.7°). After sputtering 1.5 μm AlN, several
layers are sputtered in sequence: 250 nm molybdenum as a second sacrificial layer between the
resonator and the top electrode, 400 nm aluminum as the top electrode, 20 nm molybdenum as a
barrier layer between aluminum and oxide, and lastly, 1.2 μm PECVD oxide deposited at 300 ˚C
to serve as a hard mask, yielding the cross-section of (step #3). The 20nm molybdenum between
aluminum and oxide first prevents aluminum from reacting with PECVD oxide during
deposition, and second, prevents the remaining oxide mask from contacting the top electrode
after release, which may degrade Q. Figs. 4-10(a) and (b) show photos after blanket PECVD
oxide deposition on blanket 120nm-thick aluminum with patterned titanium electrodes and
blanket AlN underneath, with and without 20 nm thick Mo as a barrier layer between aluminum
and oxide layers, respectively. It clearly shows that aluminum surface becomes rough after oxide
deposition. Note that, unlike piezoelectric resonators with contacting electrodes, the roughness
on the aluminum electrodes‘ top surfaces will not affect Q of the capacitive-piezo resonators, as
the electrodes are separated from the resonant body. However, the smooth surface is critical to
facilitate lithography resolution and etching for 1µm-thin beams.
89
The oxide mask is then patterned using a CF4/CHF3 RIE that stops on the 20 nm
molybdenum barrier layer (step #4), followed by dry etch of the film stack of Mo/Al/Mo/AlN
without breaking vacuum (step #5). By tuning the process gas ratios (Cl2, BCl3, O2), high etch
selectivity is achieved among different thin films, which is critical to the following steps of this
process.
Anchors are formed by refilling trenches with conductive materials. Instead of depositing a
conformal layer followed by etching (the ‗top-down‘ approach), which usually requires
evaluated temperatures, electroplating (the ‗bottom-up‘ approach) is a low-temperature solution
for refilling high-aspect-ratio trenches. To prepare the wafer for electroplating, 20 nm
molybdenum is sputtered to electrically connect the whole wafer by connecting the individual
molybdenum patches (step #6). This sputtering is performed at a lower chamber pressure (3
mTorr) to prevent sidewall coverage. After patterning thick photoresist, molybdenum within the
trenches is dry etched to expose Ni on interconnects (step #7) and the nickel anchor is
electroplated from the underlying nickel seed layer at 60 °C (step #8). For resonator arrays,
filters, and wine-glass disk resonators, another lithography and etch step is used to remove
oxide/molybdenum/aluminum from coupling beams and disk areas without electrodes (step #8,
step #9, and step #10). After a simple lithography step to cover the exposed isolation
oxide/nitride layers with photoresist, the thin molybdenum layer and the remaining oxide mask
are removed by dry etching (step #10), and the device is released in XeF2/N2 mixed gases. After
sacrificial molybdenum is completely etched, both the top electrode and the AlN ring are entirely
suspended from each other and supported via the nickel anchor (step #11). Contactless electrodes
eliminate the need for bimorph films (i.e., contacting electrode-AlN films) required in
conventional piezoelectric resonators and avoid issues commonly associated with bimorph films,
such as warping, stress relaxation, and film lamination. XeF2 etches molybdenum selectively
over aluminum, nickel, and AlN.
90
Cross Section c
Cross Section b
Cross Section a
AlN
Suspended
Top
Electrode
(a-1)
Coupling Beam
Anchor
(b-1)
(c-1)
(1) Deposit 250nm-oxide/200nm-nitride isolation layer and lift off 30nm-Al/70nm-Ni as the
bottom electrodes and interconnection layers with I-line PR and LOR3A (mask-1).
(a-2)
(b-2)
(c-2)
(2) Sputter 250nm molybdenum. Pattern (mask 2) I-line PR and wet etch in pre-mixed aluminum
etchant at 50°C. Strip PR.
(a-3)
(b-3)
(c-3)
(3) Sputter the following thin films in sequence: 1.5 µm AlN, 250 nm molybdenum, 400 nm
aluminum, and 20 nm molybdenum. Finally, deposit 1.2 µm PECVD oxide at 300°C.
(a-4)
(b-4)
(c-4)
(4) Pattern (mask 3) I-line PR. Dry etch oxide in CF4/CHF3 gas. Etch stops on molybdenum.
Strip PR.
Fig. 4-9: A WGD resonator array with the fabrication process of each cross-section depicted
blow. a: areas without top electrodes, such as coupling beam of resonator arrays and filters; b:
edges of the disk and areas with part of the top electrodes removed; c: anchors.
91
(a-5)
(b-5)
(c-5)
(5) Use the oxide as hard mask to dry etch molybdenum/aluminum/molybdenum/AlN, all with
chorine based chemistry but different recipes. Etch stops on molybdenum.
(a-6)
(b-6)
(c-6)
(6) Sputter 20nm molybdenum at low pressure (3 mTorr) to electrically connect the whole wafer
for electroplating. This sputter step is done at low pressure to prevent molybdenum deposited on
the side-walls and within the trenches.
(a-7)
(b-7)
(c-7)
(7) Pattern (mask 4) thick PRS 220 and dry etch molybdenum within the trenches to expose the
underlying nickel seed layer for nickel electroplating. Strip remaining PR. Need to repeat twice
to etch through the molybdenum layer as the molybdenum dry etch process, which is mixed O2
and Cl2, gives little selectivity to PR.
(a-8)
(b-8)
(c-8)
(8) Spin coat 2µm G-line PR, soft bake at 90°C for one minute, Spin coat another 1.5µm G-line
PR, soft bake at 90°C for one minute. Pattern (mask 4) to form PR mode. Isotropic oxygen
plasma etching at low power (50W) to remove possible PR residuals within the trenches.
Electroplate nickel to refill the trenches to form anchors.
Fig. 4-9-3: Step 5 to step 8 of the fabrication process.
92
(a-9)
(b-9)
(c-9)
(9) Spin coat 2µm G-line PR, soft bake at 90 °C for one minute, Spin coat another 1.5µm G-line
PR, soft bake at 90°C for one minute. Pattern (mask 5) and expose areas where the top electrodes
need to be removed.
(a-10)
(b-10)
(c-10)
(10) Etch 20nm molybdenum, the remaining (~200nm thick) oxide layer, 20nm-molybdenum,
and 400nm-aluminum. Etch stops on the molybdenum between the AlN and aluminum electrode
layers. Strip PR.
(a-11)
(b-11)
(c-11)
(11) Spin coat 2µm G-line PR, soft bake at 90°C for one minute, Spin coat another 1.5µm G-line
PR, soft bake at 90°C for one minute. Pattern (mask 6) and develop in CD-30 to cover the
exposed isolation layers.
(a-12)
(b-12)
(c-12)
(12) Dry etch 20nm-molybdenum and the remaining (~200nm thick) oxide layer. Etch stops on
the molybdenum between the AlN and aluminum electrode layers. No PR is required for this
etch step, as the exposed molybdenum layer on areas etched in the last step, where
molybdenum/oxide/ molybdenum/aluminum have been removed, and the electroplated nickel
anchor protects the underlying layers.
(a-13)
(b-13)
(c-13)
(13) Dry release in XeF2. Strip PR after release.
Fig. 4-9-3: Step 10 to step 13 of the fabrication process.
93
4.4.2 Characterization of Lift-off Process
Among many factors that affect the c-axis orientation of sputtered AlN, which can be
gauged by the angle of full-width-half-magnitude (FWHM) of the (002) peak in X-ray
diffraction measurements, substrate surface roughness is the most critical one. In this
(b) Al / PECVD OX
(a) Al / Mo / PECVD OX
Fig. 4-10: Photos of 300C PECVD oxide deposited on wafers with patterned features and blanket
aluminum as the topmost layer. (a) The surface is rough after oxide deposition. (b) Smoother
surface is obtained with a 20 nm molybdenum barrier layer that protects the aluminum layer.
PR
PR
Lift-off in
ultrasonic bath
Substrate
(a) Lift-off with positive photoresist
PR
PR
Lift-off
Substrate
(b) Lift-off with negative photoresist
PR
PR
Substrate
Substrate
Lift-off
Substrate
(c) Lift-off with double shielding layers
Substrate
Fig. 4-11: Different PR features affect the results of the metal patterns after lift-off: (a) with
sloped positive-PR; (b) with concave negative PR; (c) a combination of (a) and (b) with sloped
top layer and concave bottom layer.
94
capacitive-piezo process, even though molybdenum is used as the sacrificial material to
enhance the sputtered AlN quality, which will be discussed in more detail in 4.2.1.2, the
roughness on the substrate surface and the bottom electrodes will affect the roughness of the
sacrificial molybdenum sputtered on them. To pattern the bottom electrodes without
increasing surface roughness on the substrate, wet etching is preferred over plasma dry
etching. However, wet etching is not a suitable for patterning high-frequency devices with
1µm interconnecting signal lines, such as 1GHz ring filters. Another solution is lift -off.
In the simplest lift-off process, where positive PR is used, as shown in Fig. 4-11(a),
metal is deposited both on top and side-walls of PR patterns and on the areas not covered by
metal. Metal patterns on the substrates are then created by etching PR in an ultrasonic bath,
where metal deposited on the PR sidewalls will tear apart from the metal adhered to the
substrate once the underlying PR is etched away. This physical breaking process leaves
rough edges on the metal patterns, shown in Fig. 4-11(a).
Logically, obtaining smooth edges of the metal patterns is not possible as long as the
metal deposited on the substrate is connected to the metal on the PR sidewall. Directional
metal deposition, such as evaporation, and reverse PR sidewall profile provided by negative
PR, shown in Fig. 4-11(b), or double layer PR stack, such as the PR stack shown in Fig. 411(c) with I-line as the top layer and G-line as the bottom layer, can solve this issue. The
above two common solutions, however, are difficult to achieve pitches smaller than 2 µm.
A specially designed PR for this purpose, LOR3A, is proven to provide both smooth
metal edges and pitches as small as 500nm. Fig. 4-12(a) shows the SEM cross-section of the
PR stack and metal deposited before lift-off. The cross-section of a strip after metal
evaporation and before lift-off shows the concaving features of the bottom layer PR effectively
separates metal traces and metals on PR to be removed. In fact, no ultrasonic bath or agitation
is required for this lift-off. Figs. 4-12(b)~(c) show zoomed-in SEM on a 1 µm signal line
with smooth edges. Note that LOR3A only works for TMAH-based developers (e.g., works
for I-line developer OPD4262 but not G-line developer CD-30), which etches aluminum.
The final PR profile is a combination of many process factors, among which LOR3A
thickness, soft-bake temperature, exposure time, and the developing time are the most
important. To characterize the lift-off process for 30nm Al/70nm Ni, the thickness of
LOR3A is fixed at ~300nm and the stepper exposure time and developer time are calibrated
to the best results for 1.2µm I-line on 300nm LOR3A and nitride/oxide layers, leaving
LOR3A soft bake temperature as the only variable. A series of experiments are run to
determine the best soft-bake temperature with the following steps:
1. Spin 300 nm LOR3A. The challenging part here is to hand-spin LOR3A, which is
very fluidic, to a film only 300 nm thick. LOR3A must be applied to the center of the
wafer and any bubbles in the pipette or particles on the wafers can lead to nonuniform films.
2. Soft-bake LOR3A at various temperatures (150~180°C) for 300 seconds.
3. Spin 1.2 µm I-line and soft-bake at 90°C for 60 seconds. Note that this soft-bake
time is much lower than the one in step 2 and will not affect LOR3A underneath Iline PR.
4. Expose the wafer, post-exposure bake at 120°C for 60 seconds and develop in OPD95
PR
PR
Lift-off
Substrate
Substrate
200nm
I-line
PR
Zoom-in
Lift-off
Metal
LOR3A
(a)
(c)
(b)
Fig. 4-12: (a) The SEM cross-section of a strip after metal evaporation and before lift-off shows
the concaving features of the bottom layer PR effectively separates metal traces and metals on
PR to be removed. (b) Smooth metal edges after lift-off. (c) Zoomed-in view of the critical
part of the lift-off process with 1 µm pitch.
4262 for 60 seconds. No hard-bake is required.
5. Evaporate 100 nm thick metal on the wafer.
6. Lift-off the metal in PG Remover or PRS 3000 at 80°C.
Fig. 4-13(c) and Fig. 4-14(c) examine the metal interconnects feeding into the anchor at
the center of a disk and ring, respectively. In both cases, small pitches are preferred to
minimize the discontinuity of the bottom electrodes and the series resistance associated to
the signal lines. The metal pattern is wider than desired (i.e., too much LOR3A undercut) at
170°C of soft-bake temperature and narrow than desired (i.e., too little LOR3A undercut) at
180°C. The best soft-bake temperature is 175°C. At this temperature, 1µm metal traces with
1µm pitches are resolved with 100% yield, as shown in Fig. 4-13(a)-(b) for a disk resonator
filter and Fig. 4-14(a)-(b) for a ring resonator array.
Another common issue with metal films is poor adhesion. A disk-array filter, as shown
in Fig. 4-13(a), has 1µm wide signal lines spanning across the array. Such narrow and long
metal traces suffer from poor adhesion to the substrate, shown in Fig. 4-15(a). This issue is
resolved with dehydrating baking right before metal deposition, shown in Fig. 4-15(b). The
dehydrating baking temperature should be kept below 120°C to prevent distortion of the PR
stack profile for lift-off.
96
Zoom-in
(a)
(c-1) 170˚C Soft Bake
(b)
Fig. 4-13: Characterization of lift-off process focusing on the small pitches required for the
bottom electrodes and interconnects of a disk array filter.
(a)
(b)
Fig. 4-14: Characterization of lift-off process focusing on the small pitches required for the
bottom electrodes and interconnects of a ring resonator array.
97
Zoom-in
10μm
10μm
2μm
(c)
(b)
(a)
Fig. 4-15: (a) A narrow and long metal traces suffers from poor adhesion to the underlying
isolation nitride layer after lift-off; (b) dehydration bake solves the adhesion problem; (c)
SEM zoomed-in on the 1 µm metal trace.
4.4.3 AlN and Metal Sputtering
Unlike piezoelectric resonators with contacting electrodes, where AlN is sputtered on
patterned metals (i.e., the bottom electrodes), AlN is sputtered on the sacrificial materials
for capacitive-piezo resonators. In the first and second attempts for fabricating capacitivepiezo resonators, PECVD polycrystalline germanium deposited at 350°C and sputtered
titanium are used as sacrificial materials, respectively. It has been observed that the surface
roughness of poly-crystalline germanium is too large (>10 nm) for good AlN c-axis
orientation. Sputtered metal, on the other hand, offers a smoother surface, on the order of
5 nm. The fabrication which used titanium as the sacrificial material eventually failed at the
last release step due to insufficient etch selectivity of titanium to the isolation layers of
nitride and oxide in XeF 2. Molybdenum has therefore been adopted to replace titanium for
its high etch rate comparable to silicon in XeF 2. Interestingly, it has been observed that even
with equal metal film surface roughness, film stress, and thickness, AlN sputtered on
blanket titanium, compared to AlN on blanket molybdenum, has better c-axis orientation
and less tensile stress. The obvious difference of the two films is conductivity –
molybdenum is 7.9x more conductive than titanium. Realizing that AlN can be sputtered
with good c-axis orientation on patterned metals of even more conductive films such as
aluminum, AlN should be able to be sputtered on patterned molybdenum. The first
molybdenum layer, shown in step #2 of Fig. 4-9, is patterned into a patch for each device, as
shown in Fig. 4-16(a) with simple wet etch of aluminum etchant (pre-mixed 80% H3PO4,
5% HNO3, 5% CH3COOH, 10% DI water) at 50°C. X-ray diffraction (XRD) measurements
show that with these square patterns, sputtered AlN shows FWHM of ~1.7° and stress
within ±50MPa. Note that the mask pattern is designed such that molybdenum still covers
>99% of the entire chip area after etching. Therefore, X-ray diffraction measurement, which
covers about 4mm2 areas around the center of the wafer, faithfully reflects AlN quality on
the molybdenum rather than on the isolation layers. Patterning metal into patches probably
helps relax the stress within metal films as it heats up during AlN sputtering.
Fig. 4-16(b) shows cross-sectional view of AlN sputtered on 180 nm molybdenum,
clearly showing the closely-packed columnar structures. It is found that slight in-situ sputter
etch with argon immediately before Mo sputtering improves the orientation of the Mo (110)
98
Device 2
Device 1
Mo
Device 3
Mo
Mo
Mo
AlN
180nm Mo
Si Substrate
200nm
Nitride
Nitride
(b)
(a)
Fig. 4-16: (a) the first sacrificial molybdenum layer is patterned into patches covering
individual devices to improve the sputtered AlN quality; (b) SEM cross section of AlN
sputtered on 180nm thick, patterned molybdenum.
plane and for the desired (002) AlN growth on them. Too much sputter etching, however, results
in a rough surface and degrades AlN quality.
Stress control of all of the thin films sputtered in this process is important f or two
reasons. First, as opposed to PECVD films with equal film stress acting on both sides of the
wafer, material is only sputtered onto one side of the wafer. Large film stress can therefore
bow the wafers, making it difficult for fine alignments across the wafer at the following
lithography steps. Second, after release, both the AlN resonator and the top suspended
electrodes are suspended only by the anchor and are separated by small gaps. If the
electrodes and AlN resonators contact with each other due to relaxed film stress, Q will be
degraded, probably even lower than AlN resonators with contacting electrodes with better
resonator-electrode interfaces.
To confine the thin film stress to ±20 MPa, all of the metal films sputtered in this
process are performed in a Novellus sputtering system, which provides three variables to
tune the metal film stress: sputtering power, pressure, and substrate heating. As a rule of
thumb, more tensile film stress can be obtained by increasing the sputtering powe r and
increasing the substrate temperature.
4.4.4 AlN and Molybdenum Dry Etching
The Berkeley Microlab has long and successful history of processing AlN. However,
AlN patterning has been limited to a minimum width and via diameter of ~3µm for AlN
films thicker than 1.5 µm, due to lithography and etching capabilities. This process used Iline lithography and developed new recipes at the Centura metal etch chamber to enable 1
µm-wide AlN structures for supporting beams of resonators, and 1µm-radius vias for
anchors. Fig. 4-17(a)~(c) show SEMs of the patterned 2µm thick AlN structure of a ring
99
10μm
Zoom-in
1μm
(a)
(b)
Zoom-in
Radius
= 0.8μm
2μm
2μm
(d)
(c)
Fig. 4-17: SEMs of patterned AlN structures which are 2 µm high, featuring 1 µm wide
beams in (b) and a via with 0.8 µm radius in (d).
resonator array with 1µm-wide coupling beams next to 1µm-wide notches and 1µm-wide
supporting beams leading to a 1µm-radius via at the center. Vias with radii as small as 0.8
µm are also successfully resolved at the center of disk resonators, shown in Fig. 4-17(d).
Both AlN and aluminum can be etched by chlorine based chemistry, with the etch rate of
aluminum larger than that of AlN, while molybdenum provides a good etch stop for chlorine
based chemistry dry etch. However, with a specific ratio of mixed oxygen and chlorine,
molybdenum can be etched at up to 200nm/min while the addition of oxygen retarded the
etch rate of AlN, aluminum, and oxide. Table 2 lists the dry etch recipes for these materials
and their selectivity. For each column, the blue field indicates the target material and the
yellow fields indicate the materials where high etch selectivity is required in various steps
throughout the fabrication process. In particular, good etch selectivity among these films are
important in step #5, where AlN etch stops on molybdenum and nitride, in step #7, where
molybdenum etch stops on nickel within the trenches, in step #10, where aluminum etch
stops on molybdenum, and in step #12, where oxide etch stops on molybdenum, nickel, and
nitride. Note that because oxygen plasma is used in the molybdenum etch, photoresist ashes
quickly (573 nm/min) and may leave residuals on the surface due to reaction of oxygen,
chlorine, and PR. After step #4 (oxide hard mask etching), the remaining PR is stripped
100
Table 4-2: Etch rates of different materials in nm/min.
1. Molybdenum etch (in Centura-Metal chamber): Cl 2=90 sccm, O2=30 sccm, RF
power=900 W, bias power=100 W, pressure=10 mTorr.
2. AlN etch (in Centura-Metal chamber): Cl 2=90 sccm, BCl 3=35 sccm, Ar=10 sccm, RF
power=900 W, bias power=100 W, pressure=10 mTorr.
3. Aluminum etch (in Centura-Metal chamber): Cl2=70 sccm, BCl 3=45 sccm, Ar=10 sccm,
RF power=900 W, bias power=80 W, pressure=10 mTorr.
4. Oxide Etch (in Centura-MXP): CF4=15 sccm, CHF3=45 sccm, Ar=150 sccm, RF
power=700 W, pressure=200 mTorr.
5. Oxide Etch (in Lam2): CF 4=45 sccm, CHF3=15 sccm, Ar=50 sccm, RF power=800 W,
pressure=300 mTorr.
Mo
AlN
Al
Ni
I-Line
PR
Mo Etch
330
<3
<3
8
573
3
5
9
<3
AlN Etch
42
250
630
14
345
70.5
102
125
45
Al Etch
Oxide Etch
(Centura-MXP)
Oxide Etch
(Lam2)
20
90
550
11
278
36
70
117
23
N/A
N/A
N/A
N/A
79.4
280
380
472
120
<3
<3
<3
<3
36.7
243
315
341
110
300˚C PECVD 250˚C PECVD 200˚C PECVD
Nitride
Oxide
Oxide
Oxide
before the etching continues. As shown in Table 4-2, PECVD oxide deposited at 300°C,
compared to 250 °C and 200°C, gives higher selectivity and minimizes the required oxide
thickness as a hard mask. For PECVD oxide deposited at temperatures higher than 300°C,
the selectivity will be better, but molybdenum fails to be an effective barrier layer between
the aluminum and oxide layers.
4.4.5 Nickel Electroplating
To form anchors by electroplating nickel from the bottom of the trench is a critical step
– two fabrication runs have failed at this step. A successful anchor refill relies on careful
control and characterization of the following factors. Fig. 4-18 summarizes the possible
failing mechanisms of this step.
1. (Step #6) 20 nm molybdenum is sputtered on the wafer before electroplating to
connect all of the molybdenum patches patterned in step #2. The electroplating may
fail to refill the trenches if this thin molybdenum layer is also deposited on the
sidewalls of the structures or within the trenches, where during electroplating, nickel
will start to grow from the opening of the trench and seal it up before reaching the
bottom to form a solid anchor. To avoid this situation, this sputtering is performed at
101
low pressure (3 mTorr) to achieve a more directional sputtering by increasing the
mean-free-path of sputtered metal before it re-deposits on the wafer.
2. (Step #7) Thick G-line PR is patterned to expose only the anchoring areas. The first
molybdenum sacrificial layer at the bottom of the trenches, as shown in Fig 4-9(c-7)
is then etched away to reveal the underlying nickel seed layer for electroplating.
Given that PR is etched much faster than molybdenum and that PR is thinner on the
top of the ~4µm high structures, it takes two lithography steps using the same mask
to finish etching. The misalignment between the two lithography steps is not
harmful. In this step, as the PR pattern has an opening larger than the actual
anchoring area to accommodate alignment error, the remaining oxide hard mask
around the trench opening protects the underlying structural layers, Al and AlN, fr om
being etched. Unfortunately, the etching suffers from etch loading, where the etch
rate is faster in larger opening areas and smaller within trenches of higher aspect
ratio. After 50% overetch to ensure that molybdenum within the smallest anchoring
trench, with radius of 0.8µm, is cleared, some of the nickel seed layers underneath
the wine-glass disk anchoring trenches, with dimensions of 2 µm by 4 µm, are all
etched through, which results in only a partially filled anchor or no anchor at all for
these WDG devices.
3. (step #8) After etching of the sacrificial molybdenum layer within the trenches, the
remaining PR is stripped and G-line PR is applied and patterned again using the
same mask. Unlike the previous step, where molybdenum dry etch also removes the
PR remaining within the trenches, for this step, only a gentle oxygen plasma can be
applied before electroplating to remove PR particles without etching away the PR
pattern.
Experiments were performed first to examine whether the electroplated nickel
refills the trenches. For this purpose, dummy wafers are first patterned and hard
baked to form PR structures of the same height as the real structures on the device
wafers. The dummy wafer then went through a second lithography step for the PR
pattern for electroplating. Note that this lithography step does not affect the PR
structures already on the wafer, which is already hard baked. After electroplating
(Fig. 4-19(a)), PR is etched in an oxygen plasma to expose the entire nickel
anchors/posts (Fig. 4-19(b)), which can now be easily examined under a microscope
or SEM.
To fully expose the 3.5 µm high PR within the 3.5 µm high trenches, the PR on
top of the structure, which is only ~1 µm thick, will inevitably be overexposed. The
reflective materials, especially the thick aluminum (i.e., the top electrode layer)
underneath the remaining thin oxide hard mask and the surrounding molybdenum
layer, as shown in step #8 in Fig. 4-9(c), further deteriorates the overexposed issue.
Changing the focus of the stepper does not have a significant effect. Eventually, a
new dark field mask with patterns smaller than desired was made to accommodate
the necessary overexposure. An alternative and more elegant solution is to use
negative PR and a clear field mask with patterns only covering the anchoring areas.
The exposure dose only needs to be large enough to fully expose ~1µm thick
negative PR. The unexposed negative PR within the trenches can then be easily
washed away in developer.
102
Undesired
Electroplating
Spots
No Anchor
Formed
(c-7)
(c-8)
(a) Left: 20 nm molybdenum sputtered on the sidewalls electrically connects the other
molybdenum layers, which become undesired electroplating spots. Right: the nickel
electroplating solution may not have a chance to reach the bottom of the nickel seed
layer and electroplate upward to form an anchor before the trench is sealed up by nickel
electroplated from the undesired electroplating spots.
PR
Residual
Molybdenum
Residual
Increased
Resistivity
Poor
Support
(c-7)
Increased
Resistivity
(c-13)
(b) Left: PR and molybdenum residuals remain in the trench before nickel electroplating.
Right: PR on the interface of the nickel anchor and top aluminum electrode increases the
series resistance. After release etching of molybdenum, reduced anchor contact area with
the interconnect increases the resistance.
Ni not
electroplated
side-way
Seed Layer
Etched Through
(c-7)
(c-8)
(c) Left: While some overetch is necessary to ensure removal of the molybdenum sacrificial
layer above the nickel layer for proper anchors in different sizes of the trenches, too
much overetch breaks through the nickel seed layer and even the isolation layers. Right:
nickel does not electroplate from the exposed seed layers on the sidewalls. Nickel
anchors either form poorly or no anchor is formed.
Fig. 4-18: Three possible situations where nickel electroplating anchors will either be poorly
formed or not formed at all: (a) with metal covering the sidewalls of resonator structures;
(b) with molybdenum or PR residuals remaining in the trenches; (c) without the seed layer
on the bottom of the trench.
103
O2 Plasma
(b)
(a)
(c)
Fig. 4-19: (a)-(b) Use hard baked PR as the structure layer to characterize the nickel
electroplating process. After electroplating, oxygen plasma removed both the hard baked PR
structure and the PR pattern for electroplating to expose the entire nickel anchor for easy
inspection under SEM. (c) Center nickel anchor electroplated for a ring resonator on a
device wafer before stripping PR.
4. Nickel electroplating is performed with a homemade electroplating setup for 6‖
wafers. The wafer is electrically connected to the current supply via a metal clamp
attached to the flat of the wafer. The average electroplating rate across the wafer is
proportional to the current magnitude, but electroplating is ~1.4x faster at areas close
to the metal clamp than the areas on the other end of the wafer due to resistance. This
issue is solved by first applying PR to cover the whole wafer except for a ~3mm
wide ring around the edges of the wafer, where PR is removed by running EBR (edge
beak remover) program on the PR coating track. After electroplating ~1 µm nickel on
the exposed area and stripping PR, the wafer now has a nickel ring ―clamp‖
surrounding the edges which helps conduct current to the bottom of the wafer. This
extra step reduces the electroplating rate difference to only 1.05x. This method is
better than a real metal clamp, as an electroplated nickel ring directly on the wafer
provides good contact and good conductivity, without excess mechanical stress
which may break the wafer. Note that the flat of the wafer has to remain intact and
free from metal for the following process steps in tools which use a laser flat finder.
Fig. 4-19(c) shows a successful nickel electroplating on a device wafer, where nickel
shows lighter color than other areas covered with PR, to form the center anchor of a
ring structure with the PR pattern still on the wafer.
4.4.6 XeF2 Release
In step #13, AlN etch stops on the first sacrificial molybdenum layer but etches the
isolation layers on areas not covered by molybdenum. During XeF 2 etch release, XeF 2 can
etch away the thinner isolation layers and hollow out the silicon substrate underneath the
device. To address this issue, PR is patterned to protect areas not covered by the first
molybdenum layer and removed in oxygen plasma after release.
Another area with a thinner isolation layer is the anchors of wine-glass disks. As
mentioned in 4.2.1.4, due to etch loading, this process used 50% overetch to assure
complete etching of the first molybdenum layer and to assure that the underlying nickel seed
104
layer is exposed for the contour mode ring and disk resonators with anchors of <1 µm
radius. This also etched through the nickel seed layer and part of the isolation layers in the
anchoring trenches for some wine-glass disks. These spots become an easy path for XeF2 to
etch the silicon substrate. These spots unfortunately happen randomly on wine-glass disk
resonators across each die and it is impossible to have a single mask that can work for all
die. In order to measure some of the wine-glass disk resonators with good anchors, after
step #12 and before XeF2 release, each die is individually examined and PR is applied
manually via probe tips to the anchoring areas without nickel seed layer and nickel anchors.
This solution is very time consuming, but it works.
4.4.7 Final Remarks on Fabrication
Even though Al offers high conductance as an electrode material, which is good, the
disadvantages outweigh the advantages in three ways: (1) during AlN RIE, the Al top electrode
is also etched laterally, which is a more serious problem for thicker Al electrodes due to wider
lateral diffusion path for etchant; (2) Al is highly reactive with other materials, causing problems
on the interface of Al-Mo and Al-PECVD oxide even at low process temperature. (3) Al sets the
upper limit on process temperature when local anneal is desired to release stress, in this case, on
the electroplated nickel anchor. An alternative choice of process material combination without
using Al will be using Mo as the electrodes, oxide as the sacrificial material, and releasing in HF
vapor.
4.4.8 Fabricated Devices
Fig. 4-20 and Fig. 4-21 presents SEM images of different parts of a completed 1.2 GHz
contour-mode d31-capacitive-piezo-transduced ring resonator delineating the gaps between the
top/bottom electrode and the resonator. For these devices, to reduce electrode resistance, 400 nm
thick aluminum is used as the top electrode—something that otherwise would not be permissible
in a conventional AlN resonator, since its attached electrode would mass load the resonant
structure. This feature is especially important for resonators with thinner AlN structures for
higher electrical field across the film.
Al Top
Electrode
Width=5 μm
Electroplated
Ni Anchor
(a)
10 μm
Bottom
Electrode
1.5 μm Wide
Support Beams
Electric Access
to The Top
Electrode
Rin=25.6 μm
1.5 μm Thick
AlN Ring
Anchoring
Point
(b)
Fig. 4-20: (a) Fabricated 1.2-GHz capacitive-piezo AlN ring resonator; (b) bottom electrode and
interconnect configuration, showing anchoring at the very center. The nickel anchor provides
electrical connection to the top aluminum electrode.
105
1 μm
(a)
Suspended Top Electrode
AlN Ring
Bottom
Electrode
Gaps
(b)
Suspended
Top Electrode
(c)
1 μm
Gaps
AlN Ring
Gaps
AlN Ring
a
c
b
(d)
e
f
Interconnects
10μm
Electroplated Ni
Anchor
d
g
Bottom
Electrode
(e)
AlN Ring
AlN Support Beam
3μm
Gaps
(f)
2um
(g)
AlN Ring
Bottom
Electrode
Suspended
Top Electrode
Suspended
Top Electrode
AlN Ring
Gaps
Fig. 4-21: SEM images at different parts of the same resonator confirming that the entire top
electrode and the AlN ring resonator are suspended via the electroplated nickel anchor at the
center.
106
4.5 Electrical Measurements
4.5.1 1.2 GHz Contour-Mode Ring Resonators
Fig. 4-22 presents the measured frequency response characteristics for the AlN ring resonator
of Fig. 20(a), showing fs=1.23 GHz, Q=3,073, and Rx=889 Ω at 3 mTorr. Both the input and
output are DC grounded via bias-tee‘s to avoid electrostatic forces that might pull the top and
bottom electrodes together and into the AlN resonator. Although the measured Q is still less than
predicted by material loss theory, it is still substantially higher than any other measured contourmode AlN resonator at similar frequencies, as plotted in Fig. 4-23 [30][31][32]. The etch
residuals observed in the gaps after release, as shown in Fig. 4-21, may have affected the
measured Q. Moreover, electroplated nickel anchors are mechanically weaker and more poorly
attached to the substrate than the PECVD polysilicon anchors used in previous capacitive
resonators. This may induce more anchor loss, especially at high frequencies. Finally, due to
process difficulties, the supports of the final fabricated resonators deviated from quarterwavelength dimensions, and this further reduces Q.
It should be noted that the 260 nm gap spacing used in this device is a rather conservative
design. In fact, if the gap spacing were reduced from 260 nm to the 100 nm commonly used in
capacitive (only) resonators, the impedance could be reduced to 250 Ω.
To evaluate the efficacy of building mechanical circuits using capacitive-piezo transducers,
mechanically coupled two-resonator arrays, shown in , were also fabricated and tested. Here, the
top electrode on the coupling beam is removed to electrically isolate the output from the input.
-15
Transmission (dB)
-20
-25
Simulation
-30
-35
Measured Data
Freq. = 1.23 GHz
Q = 3,073
(Rx + RP) = 889 Ω
-40
-45
-50
-55
Measurement
-60
-65
1205
1215
1225
1235
1245
Frequency (GHz)
1255
Simulation Parameters
Young’s
350 GPa
Modulus
Density 3230 kg/m3
εAlN
9.0
e31
0.7 C/m2
Q
3,073
rm
4.65x10-6 Ω
lm
1.86x10-12 H
cm
9.08x10-9 F
η
3.26x10-4
cP
9.30x10-8 F
Fig. 4-22: Measured frequency characteristic for a 1.2-GHz AlN ring resonator with dimensions
as shown in 4-20(a) and equivalent circuit of Fig. 4-2(c).
107
Quality Factor Q
3,500
This Work
3,000
[30]
2,500
2,000
[30]
[30]
[30]
1,500 [32]
[30]
[31]
1,000
[31]
500
0
0.8
1
1.2
1.4
Frequency (GHz)
1.6
Fig. 4-23: Comparison of Q‘s achieved via the capacitive-piezo AlN ring resonator of this work
versus other ~1 GHz lateral-mode AlN resonators in [30][31][32].
The measured frequency response, shown in Fig. 4-23, exhibits much less feedthrough than seen
in single-electrode devices. However, the Q is lower for this mechanical circuit than for a single
resonator, which might be caused by etch residuals atop the coupling beam formed after dry
etching the top electrode.
In particular, it is not unreasonable to expect that future capacitive-piezo equipped resonators
with better defined quarter-wavelength supports and stiffer anchors might eventually achieve the
Q‘s in the tens of thousands at GHz range predicted by theory.
4.5.2 50 MHz Wine-Glass Disk Resonator Array
The mode shape of the ring has static points only at the center of the ring, which is difficult
to access. The support beams of the 1.2 GHz ring resonators described above are attached to the
resonator at the positions with the largest amplitude. Therefore, the resonators suffer from anchor
loss and the anchors are made as small as the process allows, in this case, 1.8 µm in diameter, to
minimize the anchor loss. As a result, the anchors of the 1.2 GHz ring resonators are not strong
enough to withstand cleaning procedures, such as ultrasonic clean, to remove the etch residuals
from the resonator surfaces and from within the gaps. To tap the Q of sputtered AlN, wine-glass
disk (WGD) resonators with larger anchoring areas and support beams attached to the quasistatic points are also measured after each cleaning step to monitor Q increases. It is north noting
that the composite and equi-volume nature of the wine-glass mode shape, where both
longitudinal and shear strain are present and out of phase, makes it difficult to excite and sense
the disk with the piezoelectric effect and to obtain high coupling as the ring resonator described
in the previous section. After release, the edges of the top electrodes, where the maximum
displacement occurs, curl up perhaps due to stress, as shown in Fig. 4-25, which makes the
effective gap spacing larger and effective coupling even weaker. The above factors together
reduce the induced motional current relative to the feed-through current. To obtain a series
108
-30
30um 30um
BottomBottom
λ/2
λ/2
Electrode
Electrode
Coupler
Coupler
Gnd. Gnd.
Gnd. Gnd.
(a) Output
(a) Output
signal signal (b)
-35
Etch Etch
Residual
Residual
-40
-45
-25
Transmission (dB)
Al top electrode
Al top electrode
AlN ring
AlN ring
-50
AlN ring
Etch
Residual
Al top electrode
Transmission (dB)
Al top electrode
Freq.=1.0 GHz
Q=1,055
(Rx+RP) = 2 KΩ
-30
-35
-40
-45
-50
1um
(c) 0.99
0.995
1
1.005
1.01
1.015
Frequency (GHz)
Fig. 4-24: (a) SEM of a capacitive-piezo ring resonator array with λ/2 coupler; and (b) top-view,
zoomed-in SEM showing how the electrode is removed from the coupler to electrically isolate
the output from the input. (c) Measured frequency characteristic for the resonator in (a)
confirming suppression of the parallel resonance peak.
resonant peak free from the anti-resonant peak for more accurate Q measurement, feed-through
currents must be reduced accordingly. Considering the rather large size of the disk and the
suspended top electrode, to better combat the possible vertical residual stress gradient of the Al
electrodes, it is preferred that the top electrodes are supported on both ends (like a clamp-clamp
beam), rather than supporting input and output top electrodes individually with each anchor (like
a cantilever), as a 2-port single resonator required. Instead, two-resonator arrays were measured.
With proper coupling beam design, the Q‘s of an array have been shown to take the value of
individual resonators.
109
-30
-35
-40
-45
-50
Al top electrode
Al top electrode
1um 1um
0.99
0
(c) 0.99(c) 0.995
(b)
Fr
-25
ottom
ectrode
)
-25
Transmission (dB)
Input signal
Gnd. Gnd.
Gnd. Input
Gnd. signal
DC = 0V
Network Analyzer
DC = 0V
Bias-Tee
Bias-Tee
Edges of the top
electrodes curl up
Input
Output
GND
Bottom
Electrode
50 μm
AlN
Top
Electrode
Coupling Beam
Anchor
GND
10 μm
(a)
Ni
Anchor
Support
Beam
Output
Input
XeF2
Dry Etch
Top Electrode
1.5 μm Thick AlN
AlN
AlN
Sacrificial Mo
Gaps
Top
Electrode
(c)
(b)
Gap
Gap
Gap
AlN
AlN
(e)
Gap
Gap
AlN
Bottom Electrode
Gaps (d)
Columnar
structure
and
Gap
close pack
grains shown
on AlN surface
AlN
Gap
Gap
(e)
Fig. 4-25: (a) Fabricated AlN disk resonator array and the measurement setup which yields the
measured frequency spectrum in Fig. 4-27. (b) and (c) zoomed-in views on the anchor before and
after XeF2 dry release, respectively; (d) side-view of the resonator edge, showing the whole disk
lifted between the top and bottom electrodes; (e) zoomed-in SEM figures on the generated gaps
after release. After numerous cleaning steps, etch residuals on the AlN disk are noticeably
reduced but not completely gone, which can degrade the quality factor.
110
The resonators with support beam width of 1 µm, 1.5 µm, and 2 µm, as shown in Fig. 4-26,
are measured to show Q of 8,193, 7,292, and 6,061 after XeF2 release, respectively, shown in Fig
4-27. Note that at this point, photoresist to protect nitride/oxide isolation layers during release is
present on the chip. After oxygen plasma clean, EKC-270 dip, and critical point drying in
methanol, Q increases for all three cases. After annealing at N2/H2 at 500°C for 30 minutes, Q
further increases to 12,748 for the resonator with 1 µm support beams, posting the highest ever
measured for sputtered AlN resonators. Q is higher than 10,000 even for resonators with support
beams of 1.5 µm. The effects of anneal on enhancing Q are not definite. It has been observed that
particles inside the gaps close to the edges of the disk, as shown in Fig. 4-25(e), decrease after
anneal. Moreover, anneal relaxes the stress of electroplated nickel, an approach used before to
enhance Q of a comb-drive resonator made of electroplated nickel by 3.5 times [33]. It is also
possible that anneal modifies the Ni-AlN interface such that phonon transfer to the substrate, and
subsequent dissipation through the nickel anchor, is reduced. Whether anneal at even higher
temperatures will further increase Q is unknown because aluminum electrodes limit the
allowable anneal temperatures.
Bottom Electrode
Top
Electrode
Top
Electrode
Top
Electrode
AlN
Disk
Ni
Anchor
Fig. 4-26: Zoomed-in SEM figures on the anchors of fabricated wine-glass disk resonator with
various support beam width as indicated with arrows in the figures: (a) 1 µm; (b) 1.5 µm; (c) 2
µm. All the other geometry are the same for these disk resonators.
Table 4-3: Summary of the measurement data of 50MHz WGD capacitive-piezo resonators with
various support beam width after various cleaning and anneal treatments.
Support Beam Width Ws = 1 μm
Support Beam Width Ws = 1.5 μm
fo
S21 Peak Rx
(MHz) (dB)
(KΩ)
#
Q
8,193
50.958
-37.2
7.14
1
2
8,942
50.967
-36.4
6.51
2
3
12,748 50.990
-33.3
4.52
#
Q
1
Support Beam Width Ws = 2 μm
fo
S21 Peak Rx
(MHz) (dB)
(KΩ)
#
Q
7,292
51.042
-38.2
8.03
1
6,061
50.913
-39.8
9.67
7,734
51.049
-37.7
7.57
2
6,366
50.931
-39.4
9.23
3 10,218 51.883
-35.3
5.72
3
7,076
50.950
-38.4
8.22
111
fo
S21 Peak Rx
(MHz) (dB)
(KΩ)
-30
As Released
S21 (dB)
-40
-50
1μm: Q = 8,193
2 μm:
Q = 6,061
1.5μm:
Q = 7,292
-60
-70
-80
-90
50.7
-30
O2 Plasma
50.9
S21 (dB)
EKC-270 80˚C Dip
51.3
Q = 8,942
-40
-50
51.1
Q = 6,366
Q = 7,734
-60
-70
-80
Critical Point Drying
-90
50.7
-30
50.9
51.1
Q = 12,748
Anneal at 500˚C,
0.5 hour
S21 (dB)
-40
-50
51.3
Q = 10,218
Q = 7,076
-60
-70
-80
-90
50.7
50.9
51.1
51.3
Frequency (MHz)
Fig. 4-27: Measured frequency characteristics for the resonator in Fig. 4-25. The resonator Q is
still limited by the anchor loss, as resonators with thinner support beams render higher Q. In
particular, the resonators with 1.5 µm and 1 µm support beams achieve Q higher than 10,000, the
highest two data points ever measured for resonators made of sputtered AlN at any frequency.
112
4.6 References
ring resonators," in Tech. Digest., 17th IEEE Int. MEMS Conf., pp. 821-824, 2004
[2] S.-H. Lee, et. al., ―Influence of electrode configurations on the quality factor …,‖ J. Appl.
Phys, vol. 92, pp. 4062-4069, 2002.
[3] C.-L. Huang, K.-W. Tay and L. Wu, ―Effect of AlN film thickness and top electrode
materials on characteristics of thin-film bulk acoustic-wave resonator devices,‖ J. Appl.
Phys. vol. 44, pp. 1397-1402, 2005.
[4] M. Ueda, T. Nishihara, J. Tsutsumi, S. Taniguchi, T. Yokoyama,
S. Inoue, T. Miyashita and Y. Satoh, ―High-Q resonators using FBAR/SAW technology and
their applications,‖ in Digest, IEEE Inter. Microwave Symp., pp. 209-212, 2005.
[5] L. Mai, V.-S. Pham, and G. Yoon, ―ZnO-based film bulk acoustic resonator devices on a
specially designed Bragg reflector,‖ J. Applied Physics, vol. 95, pp. 667-671, 2009.
[6] S. K. Kor, P. K. Mishra, and N. D. Tripathi, "Ultrasonic attenuation in pure and doped ntype silicon," Physical Review B, vol. 10, p. 775, 1974.
[7] D. K. Pandey, D. Singh, and R. R. Yadav, "Ultrasonic wave propagation in IIIrd group
nitrides," Applied Acoustics, vol. 68, pp. 766-777, 2007.
[8] R. Tabrizian, M. Rais-Zadeh, and F. Ayazi, ―Effect of phonon interactions on limiting the fQ
product of micromechanical resonators,‖ in Tech. Dig., Transducers’07, 2007, pp. 21312134.
micromechanical wine-glass disk oscillator,‖ in Tech. Dig., IEEE Int. Electron Devices
Mtg., 2005, pp. 287-290.
[10] F. Ayazi, S. Pourkamali, G. K. Ho, and R. Abdolvand, "High-aspect-Ratio SOI vibrating
micromechanical resonators and filters," in in Tech. Digest, IEEE MTT-S Int. Microwave
Symp., 2006, pp. 676-679.
[11] S. V. Krishnaswamy, J. D. Adam, and M. Aumer, ―High-Q FBARs using epitaxial AlN
films,‖ in Proc. IEEE Int. Ultrasonic Symp., 2006, pp. 1467–1470.
[12] A. N. Cleland, M. Pophristic, and I. Ferguson, ―Single-crystal aluminum nitride
nanomechanical resonators,‖ Applied Physics Letters, vol. 79, no. 13, pp. 2070-2072, Sep.
2001.
[13] C. G. Courcimault and M. G. Allen, ―High-Q mechanical tuning of MEMS resonators using
a metal deposition-annealing technique,‖ in Tech. Dig., Transducers’05, 2005, pp. 875-878.
[14] J. Wang, J. E. Butler, T. Feygelson, and C. T.-C. Nguyen, ―1.51-GHz polydiamond
micromechanical disk resonator with impedance-mismatched isolating support,‖ in Tech.
Digest, 17th IEEE Int. MEMS Conf., 2004, pp. 641-644.
[15] C.-L. Dai, C.-H. Kuo, and M.-C. Chiang, "Microelectromechanical resonator manufactured
using CMOS-MEMS technique," J. Microelectronics, vol. 38, pp. 672-677, 2007.
113
[16] C. K Jahnes, J. Coite, J. L. Lund, H Deligiunni, A. Chinthukindi, L. P. Buchwalter, P. Fyer,
J. A. Tornello, N. Hoivik, J. H. Mugerlein and D. Seeger, ―Simultaneous fabrication of RF
MEMS switches and resonators using copper-based CMOS interconnect manufacturing
methods,‖ in Tech. Digest, 17th IEEE Int. MEMS Conf., 2004, pp. 789-792.
[17] J. Verd, A. Uranga, G. Abadal, J. L. Teva, F. Torres, J. L. Lopez, E. Perez-Murano, J.
Esteve, and N. Barniol, "Monolithic CMOS MEMS oscillator circuit for sensing in the
attogram range," Electron Device Letters, IEEE, vol. 29, no. 2, pp. 146-148, Feb. 2008.
[18] W.-C. Chen, C.-S. Chen, K.-A. Wen, L.-S. Fan, W. Fang, and S.-S. Li, ―A generalized
foundry CMOS platform for capacitively-transduced resonators monolithically integrated
with amplifiers,‖ in Tech. Digest, 23rd IEEE Int. MEMS Conf., 2010, pp. 204-207.
[19] C-C Lo, F. Chen, and G. K. Fedder, ―lntegrated HF CMOS-MEMS square-frame resonators
with on-chip electronics and electrothermal narrow gap mechanism,‖ in Tech. Dig.,
Transducers’05, 2005, pp. 2074–2077.
[20] L.-W. Hung, and C. T.-C. Nguyen ―Silicide-based release of high aspect-ratio
microstructures,‖ in Tech. Digest, 23rd IEEE Int. MEMS Conf., 2010, pp. 120-123.
[21] N. Abelé1, K. Séguéni, K. Boucart, F. Casset, B. Legrand, L. Buchaillot, P. Ancey, A.M.
Ionescu1, ―Ultra-low voltage MEMS resonators based on RSG-MOSFET,‖ in Tech. Digest,
19th IEEE Int. MEMS Conf., 2006, pp. 882-885.
[22] S. Basrour, H. Majjad, J. R. Coudevylle and M. de Labachèlerie, ―Simulation and
characterization of high Q microresonators fabricated by UV–LIGA,‖ Tech. Proc., Int.
Modeling and Simulation of Microsystems (MEM) Conf., 2001.
[23] W.-L. Huang, Z. Ren, and C. T.-C. Nguyen, "Nickel vibrating micromechanical disk
resonator with solid dielectric capacitive-transducer gap," in Proc. IEEE Int. Freq. Control
Symp. pp. 839-842, 2006.
[24] W.-L. Huang, S.-S. Li, Z. Ren, and C. T.-C. Nguyen, ―UHF nickel micromechanical spokesupported ring resonators,‖ in Tech. Dig., Transducers’07, 2007, pp. 323–326.
[25] L. Lihua, P. Kumar, L. Calhoun, and D. L. DeVoe, "Piezoelectric Al0.3Ga0.7As longitudinal
mode bar resonators," J. Microelectromechanical Systems, vol. 15, pp. 465-470, 2006.
[26] R. Besson, ―A new ‗electrodeless‘ resonator design,‖ in Proc. IEEE Int. Freq. Control
Symp. pp. 147-152, 1976.
[27] J. R. Norton and R. Besson, ―Tactical BVA quartz resonator performance,‖ in Proc. IEEE
Int. Freq. Control Symp. pp. 609-613, 1993.
[28] W. Pang, H. Zhang, H. Yu., C.-Y. Lee, and E. S. Kim, ―Electrical frequency tuning of film
bulk acoustic resonator,‖ IEEE/ASME J. Microelectromech. Syst., vol. 16, no. 6, pp. 1303–
1313, Dec. 2007.
[29] Y.-W. Lin, S.-S. Li, Z. Ren, and C. T.-C. Nguyen, ―Third-order intermodulation distortion in
capacitively-driven VHF micromechanical resonators,‖ in Proc., IEEE Int. Ultrasonics
Symp., 2005, pp. 1592-1595.
[30] C. Zuo, J. V. der Spiegel, and G. Piazza, ―1.05GHz MEMS oscillator based on lateral-fieldexcited piezoelectric…,‖ in Proc. IEEE Int. Freq. Contr. Symp., 2009, pp. 381-384.
114
[31] P. J. Stephanou and A. P. Pisano, "GHz higher order contour mode AlN annular resonators,"
in Tech. Dig., 20th IEEE Int. MEMS Conf., 2007, pp. 787–790.
[32] G. Piazza, P. J. Stephanou, and A. P. Pisano, "One and two port piezoelectric higher order
contour-mode MEMS resonators for mechanical signal processing," Solid-State Electronics,
pp. 1596-1608, 2007.
[33] W.-T. Hsu, S. Lee, and C. T.-C. Nguyen, ―In situ localized annealing for contamination
resistance and enhanced stability in nickel micromechanical resonators,‖ in Tech. Dig., 10th
Int. Solid-State Sensors and Actuators Conf., 1999, pp. 932-935.
115
Chapter 5: Q-Boosting AlN Array-Composite
5.1 Introduction
Although thin-film AlN micromechanical resonators post lower (hence, better) motional
impedances than their capacitively transduced counterparts [1], their lower Q (~1,000 vs. >
10,000 for capacitive) have long disqualified them from emerging applications that demand Q >
10,000. For example, the low-power spectrum analyzer needed at the front-end of a cognitive
radio requires small percent bandwidth filters [2] which in turn demand very high Q resonators
to avoid excessive insertion loss. As described in Chapter 1, the filter insertion loss depends on
resonator Q. To assure less than 3 dB insertion loss, the minimum required resonator Q is only
1,000 for a 1% bandwidth filter, but as high as 10,000 for 0.1% bandwidth, clearly emphasizing
the importance of Q when small percent bandwidths are needed. Unfortunately, no previous
sputtered AlN resonator has been capable of achieving Q >10,000, and so cannot be used to
realize narrow-band filters without excessive insertion loss. Rather, AlN technology has been
relegated to wide-band filter applications, where their lower Q is less consequential and their
strong electromechanical coupling enables filter termination impedances compliant with
conventional values (e.g., 50 Ω).
Interestingly, despite the fact that the highest measured Q of d31-transduced low-temperature
sputtered AlN resonators (Q = 5,830 at 43.26 MHz [3]) are 28x less than that of polysilicon
counterparts (Q = 161,000 at 61.9 MHz [4]) for the same mode shape at similar frequencies,
material loss theory predicts that the material Q of AlN should only be ~2x less than that of
silicon [5]. There are many who believe that the low Q results from the use of low-temperature
AlN sputter deposition in previous work. An alternative hypothesis, however, rejects material
loss as the primary Q-limiting loss mechanism and rather focuses on the difference between
capacitive resonators and piezoelectric resonators: in the former, the electrodes do not touch the
resonator, whereas in the latter, the electrodes attach directly to the resonator. Although attaching
electrodes to a piezoelectric resonator does maximize the electric field strength available to
generate the piezoelectric effect, it also exposes the resonator to losses inherent in the electrode
material and at the electrode-to-resonator interface. This electrode-based loss can then dominate
among dissipation mechanisms, preventing measurement of the actual material Q of AlN.
Realizing this, the work presented in Chapter 4 harnessed capacitive-piezo transducers that
separated an AlN resonator from its electrodes by small gaps, thereby eliminating electrode
losses towards a Q of 3,073 at 1.2 GHz [6] and 12,748 at 50.9 MHz [7]. This Q is higher than
previously demonstrated at similar frequencies, but still limited by the losses due to fabricationderived etch residuals.
This work circumvents the above fabrication difficulties towards finally measuring AlN
resonator Q’s closer to theoretical prediction by using a mechanical circuit-based approach that
mechanically couples electrode-equipped input/output resonators with electrode-less ones,
allowing the composite mechanically resonant structure to behave more ―electrode-less‖ when
116
the number of electrode-less resonators is much larger than the number of electrode-equipped
resonators. When this is the case, the composite resonator exhibits a higher (i.e., boosted) Q than
it would if composed of only electrode-equipped resonators, i.e., the addition of electrode-less
resonators ―boosts‖ the original Q. Using this approach, Q = 10,444 [8] is measured for an arraycomposite resonator structure that combines two electrode-equipped resonators with thirty
electrode-less ones. This 3.4x increase in Q over previous work should greatly decrease both
insertion loss in filters and phase noise in oscillators.
5.2 Q-Boosting Micromechanical Circuits
Fig. 5-1(a) presents a drawing of the Q-boosting mechanical circuit (along with its electrical
equivalent) used in this work. Here, two ―end‖ resonators, equipped with electrodes and designed
to vibrate in wine-glass mode shapes [9], are mechanically coupled by half-wavelength beams to
several ―inner‖ resonators that are electrode-less, but otherwise identical to the end resonators in
shape and dimension. The whole structure comprises a single array-composite resonator that can
be excited into mechanical resonance by applying a resonance AC voltage across the top and
bottom electrodes of one of the electrode-equipped end resonators, thereby generating a vertical
electric field that induces lateral strain via the d31 coefficient of the AlN piezoelectric material,
causing the entire structure to vibrate. The other end resonator then electrically monitors the
vibration via output currents provided by the piezoelectric effect.
Proper operation of this structure relies on the same assumption as the work of capacitivepiezo transducers, in that metal electrode-derived loss mechanisms dominate among Q-limiting
factors, and so removing metal electrodes from the inner resonators should result in much higher
Q than their end resonator counterparts. If this is the case, then energy sharing between
resonators in the mechanically-coupled structure should raise (or boost) the Q of the composite
structure to a value larger than possessed by each end resonator alone. To understand how a Qboosting circuit works, it is illustrative to consider the simplest case, where all of the resonators
in the array-composite are identical.
Electrode
Input
Resonator
Electrode-Less
Resonator
Coupling Electrode-Less
Beam
Resonator
Coupling
Beam
Output
Resonator
Fig. 5-1: A piezoelectric resonator array-composite where only one resonator on each end of the
array-composite has contacting electrodes and serves as the input and output resonators,
respectively.
117
5.2.1 Array-Composite of Identical Resonators
For a mechanically coupled micromechanical resonator array-composite, shown in Fig. 52(a), the equivalent Q and impedance of the entire array-composite can be derived either with
energy analysis [9] or with the equivalent electrical circuit analysis.
a. Energy Analysis
To quickly illustrate the Q-boosting property, consider that the Q of the composite
mechanically-coupled resonator structure is given by the total stored energy ETot summed among
all constituent resonators, divided by the total loss per cycle LTot, again summed over all
resonators. If the quality factor Qn of a given resonator n in the mechanical circuit of Fig. 5-2(a)
can be written as Qn = En/Ln, where En and Ln are the energy stored and energy lost per cycle,
respectively, for resonator n, then one can write for the case where all N array resonators have
the same stored energy per cycle Eo


N
Q Mckt
Disk 1
E
 Tot 
LTot
n 1
N
En
L
n 1 n

N  Eo

N
N
L
n 1 n
Disk 2

N

1
( Ln /E o )
n 1
(5-1)
Disk 3
Disk N
Disk 3
Disk N
(a)
Disk 1
Disk 2
Extra
Coupling
Center
Anchor
Anchor
Beam
Electrodes
Support
Beam
(b)
Fig. 5-2: (a) A resonator array-composite composed of N identical resonators mechanically
coupled to each other; (b) a resonator array-composite similar to the one in (a) except that one of
the resonators (resonator 2) has lower Q than all of the others due to excess anchor losses.
118
Use of the definition of Q then yields
Q Mckt
 1
1
1 

 N  

 
Qn 
 Q1 Q 2
1
(5-2)
For the case where the Q of all of the resonators are the same, say, Q1 = Q2 = ··· = Qn = Qo, (52) predicts that QMckt = Qo. As the half-wavelength coupling scheme is ideally lossless and the
array-composite resonator is a passive device (i.e., no energy is generated), the mechanicalcircuit Q, QMckt, should not deviate from the individual resonator.
For the case where the Q of one of the resonators, (e.g., Q2), is much less than the Q of all
other resonators, as shown in Fig. 5-2(b), where resonator-2 suffers from more extra anchor loss
due to the center stem and two more side-ways anchors, (5-2) reduces to QMckt = N×Q2.
QMckt  N  Q2
(5-3)
Therefore, when coupled with (N-1) much higher-Q resonators, Q1 is effectively boosted by
N times. In the limit as N goes to infinity, QMckt is bounded by the Q of the high-Q devices. In
other words, the larger the number of high Q electrode-less resonators coupled to a single low Q
electrode-equipped resonator, the more the entire mechanical circuit takes on electrode-less
characteristics, and the closer QMckt comes to the Q of an electrode-less AlN resonator.
b. Equivalent Circuit Analysis
The motional resistance of a micromechanical resonator (or circuit of such resonators) often
governs its utility in a given application [4]. To gauge the impact of adding coupled electrodeless resonators on the motional resistance of a pair of electrode-equipped resonators, Fig. 5-3(b)
presents the equivalent electrical circuit model for the resonator array shown in Fig. 5-3(a). Here,
the motional circuit elements that model each resonator take on values corresponding to its mass
mrn, stiffness krn, and damping crn, and the half-wavelength coupling links are modeled by T
networks of capacitors with relative values indicated. The coupling coefficients at input and
output ports associated with each electrode-equipped resonator are ηi,n and ηo,n, respectively.
This half-wavelength coupled circuit effectively places the motional elements of all resonators in
series, so the circuit reduces to that in Fig. 5-3(c), for which
m r , Mckt 

k r , Mckt 

n 1
c r , Mckt 

n 1
N
m rn
(5-4)
k rn
(5-5)
c rn
(5-6)
 i , Mckt  n1 i ,n
(5-7)
 o , Mckt  n1 o ,n
(5-8)
n 1
N
N
ne
ne
119
where mr,Mckt, kr,Mckt, and cr,Mckt are the mass, stiffness, and damping, respectively, of the
composite mechanical circuit; ηi,Mckt and ηo,Mckt are the equivalent electromechanical coupling
coefficients at the input and output ports, respectively; ne is the total number of electrodeequipped resonators in the array. Using the circuit in Fig. 5-3(c) and (5-4)-(5-8), the Q and
motional resistance of the composite mechanical circuit, QMckt and RMckt, respectively, can be
written as
Electrode
Electrode
Input
Resonator
Coupling
Beam
Electrodeless Res.
lx,1 cx,1 rx,1 1 : η cc cc η :1 lx,2 cx,2 rx,2
c
c
Coupling
Beam
ηc:1
Output Res.
cc cc 1 : η lx,1 cx,1 rx,1
c
-2cc
ηo:1
1 : ηi
-2cc
Co
Co
(a)
1 : ηi
Co
ηo:1
lx,1 cx,1 rx,1
lx,1 cx,1 rx,1
lx,2 cx,2 rx,2
Co
(b)
1 : ηi
Co
ηo:1
lx,eq cx,eq rx,eq
Co
(c)
Fig. 5-3: (a) A piezoelectric resonator array-composite and its equivalent electrical circuit where
only one resonator on each end of the array-composite has contacting electrodes and serves as
the input and output resonators, respectively; (b) a simplified version of the circuit in (b), which
can be further simplified to the circuit in (c).
120
Q Mckt 
m r , Mckt  k r , Mckt
c r , Mckt
(


N
n 1
m rn )  (

N
n 1

N
n 1
k rn )
(5-9)
c rn
and
RMckt 
cr , Mckt
 i , Mckt   o , Mckt


N
n 1
crn
 i , Mckt   o , Mckt
(5-10)
This analysis can be further generalized to an array of N resonators, all with identical
motional mass mrn and stiffness krn, among which ne resonators are electrode-equipped and (Nne) resonators are electrode-less with Q’s α times larger than the former. In this case, (5-9) and
(5-10) become
Q Mckt 
N
 Qo
ne  ( N  ne ) / 
(5-11)
RMckt 
1  ( N / ne  1) / 
 Ro
ne
(5-12)
and
where Qo and Ro are the Q and motional resistance of a single electrode-equipped resonator,
respectively. Fig. 5-4 plots QMckt and RMckt governed by (5-11) and (5-12) with ne=1 and α’s of 10
and 100, respectively, against the total number of resonators in the array, N. As the number of Qboosting resonators in the array, (N-1), increases, both QMckt and RMckt increase. However, when
α is large, as indicated by the α = 100 curve, QMckt increases almost linearly with N, while RMckt
barely changes, i.e., QMckt can be increased without significant penalty to RMckt. In fact, when
α = 100, a 30 increase in QMckt is realized with a less than 50% increase in RMckt.
It should be noted that the described Q-boosting circuit does not raise the piezoelectric
resonator FOM, given by Q·kt2. This is because while the Q boosts by N, the effective
electromechanical coupling kt2, defined in (1-38), decreases by N due to an N increase in
stiffness (or mass), as governed by (5-5) (or (5-4)). In essence, a Q-boosted AlN resonator array
trades kt2 for higher Q.
5.2.2 Coupling Resonators of Various Sizes
Q-boosting circuits can also be implemented by coupling resonators with the same resonant
frequency but with different stiffness and mass. To quickly demonstrate this, consider the
circuits in Fig. 5-5(a). The serial combination of capacitor-inductor-resistor, corresponding to the
two higher-Q resonators in the middle, can be redrawn to Fig. 5-5(b) with the same electrical
response and Q-boosting effect. In the mechanical domain, the circuits in Fig. 5-5(a) and (b)
correspond to coupling transduction resonators to more high-Q resonators with less mass and
stiffness, or less high-Q resonators with more mass and stiffness.
121
5
5
α = 100
RMckt / Ro
QMckt
Mckt / Qo
o
31
31
31
31
26
26
26
26
21
21
21
21
16
16
16
16
11
11
11
11
66
66
11
11
α = 10
11
11
11
21
31
41
11
21
31
41
Res. # N (w/ ne =1)
(a)
4
4
α = 10
3
3
100
α == 100
2
2
1
1
1
1
11
11
21
21
31
31
31
31
nee =1)
=1)
Res. # N (w/ n
41
41
41
41
(b)
Fig. 5-4: (a) and (b): theoretical plots of (5-11) and (5-12), respectively, with ne=1, showing how
the overall Q and impedance of the composite mechanical circuit, QMckt and RMckt, change as the
number (N-1) of Q-boosting resonators in the array increases. The QMckt increases more with less
impedance penalty when α is large.
Indeed, from (5-4)-(5-6), the parameters that determine QMckt is the summation of the mass,
stiffness, and damping factor of individual resonators in the array, regardless the total number of
resonators. Q-boosting circuits are most effective when the higher-Q resonators have larger
stiffness and mass than the lower-Q resonator.
The following discussion considers an array-composite where the higher-Q resonators have
different Q, stiffness, and mass. To simplify the case, all of the Nlow lower-Q resonators are
assumed to be identical. The Nhigh higher-Q resonators have stiffness, mass, and Q as
mri   i  mr ,o
(5-13)
kr , i   i  kr , o
(5-14)
Q   i  Qo
(5-15)
where mr,o, kr,o, and Qo are the mass, stiffness, and Q of Nlow identical lower-Q resonators,
respectively. βi and αi are the ratio of stiffness/mass and Q between the higher-Q and lower-Q
resonators, respectively. Note that mr and kr need to have the same ratio, βi, relative to mr,o and
kr,o, in order to maintain the same resonant frequency. Using the equation of Q, cri can be
expressed as
122
mr  kr
cri 

Q
 i mr   i k r  i m r  k r  i
 
  c r ,o
i  Q
i
Q
i
(5-16)
Therefore, the overall Q is, according to (5.4.1)
QMckt 
(

N
mrn )  (
n 1

N 

N 

N
k )
n1 rn
N

( N low 

low
1
N high
low
1
i
i /i
1
 i )mr ,o  ( N low  1
( N low 
c
n1 rn
N high
N high
N high

N high
1
 i )kr ,o
 i /  i )c r ,o
(5-17)
 Qo
The modifier of the last term in (5-17) approaches unity and there is minimal Q-boosting
effect when
lx,1 cx,1 rx,1
1 : ηc cc cc ηc:1
lx,2 cx,2 rx,2
-2cc
ηo:1
1 : ηi
-2cc
1 : ηc cc cc ηc:1 lx,N cx,N rx,N
Co
Co
(a)
lx,1 cx,1 rx,1
1 : ηc cc cc ηc:1 (N-1)·lx,2 (N-1)·cx,2 (N-1)·rx,2
ηo:1
1 : ηi
-2cc
Co
Co
(b)
Fig. 5-5: (a) equivalent circuit of a resonator array-composite where one resonator serves as both
the input and output resonator and the remaining (N-1) resonators without electrodes have higher
Q; (b) a modification of the circuit in (a) by combining (N-1) higher-Q resonators into a single
resonator with larger mass and stiffness.
123

N high
1
 i  N low
(5-18)
One of the examples of resonators of identical resonant frequency but different stiffness and
mass is a contour-mode ring resonator with the same ring width but various average radii. The
frequency equations for the contour-mode ring shape can be found in [10] When the average
radius of a ring is much larger than its width, the resonant frequency is determined by the width
and is independent of the radius, which suggests that both the motional mass and the stiffness are
proportional to the radius. This can be implemented as several concentric rings to save layout
space, such as shown in Fig. 5-7(a) and (b) with simulation parameters of each ring resonator
listed in Table 5-1. The length of each coupling beam and the width of the ring are 4.87 µm and
10 µm, respectively. The average radius of each ring therefore differs by the ring width plus the
half-wavelength coupling beam, or 14.87 µm. Fig. 5-7 shows three different coupling and
transduction schemes with comparable layout areas. The array-composites in Fig. 5-7 (a) and (b)
have electrodes on the inner-most ring and the outer-most ring, respectively, and are otherwise
the same. Assuming all of the Q-boosting electrode-less resonators exhibit Q larger than Q of the
electrode-loaded resonator by 100 times (i.e., α1 = α2 = … = 100 in (5-13) to (5-17)), Table 5-1
compares the mechanical circuit Q and impedance of each resonator array-composite in Fig. 5-7
compared to those of a transduction resonator of 40 µm average radius. It clearly shows that by
coupling resonators with larger mass and stiffness, the Q boosting factor is larger with little
penalty on impedance increase.
Ideally, it is possible to couple one low-Q resonator with a massive, stiff high-Q resonator of
the same frequency to boost the overall Q. There is an immediate advantage of this approach: a
system with fewer degrees of freedom has fewer spurious modes to suppress and fewer
resonators to trim to obtain a certain target frequency, if necessary.
dB(S(3,4))
dB(S(5,6))
dB(S(13,14))
dB(S(7,8))
Loss (dB)
Insertion
dB(S(11,12))
-5
N=1
N=3
-10
-15
-20
N=5
-25
N=9
-30
-35
-40
-45
-50
154.3
N = 16
154.7
155.1
155.5
freq, MHz(MHz)
Frequency
Fig. 5-6: Simulation results of the circuits in Fig. 5-5 with varying N.
124
155.9
156.3
Electrode
(a)
(b)
Ring # 1
Ring # 3
Ring # 2
Ring # 5
Electrode
Ring # 4
(c)
Electrode
Fig. 5-7: Three resonator-composites that occupy the same areas. The design parameters of each
ring is listed in Table 5-1. (a) a concentric rings configuration with electrodes on the smallest
ring; (b) a concentric rings configuration with electrodes on the largest ring; (c) a chain of
resonators each has the same size as the smallest ring in (a) and (b).
Table 5-1: Design parameters of rings of the same width but various average radii, as shown in
Fig. 5-7(a) and (b).
Ring
#.,
n
Ave.
Res. Freq., Res. Freq. Stiffness,
Radius,
f (MHz) Ratio (fn/f1) krn (N/m)
RAve (µm) o
Stiffness
Ratio
(krn/kr1= βi)
Mass, mrn
(kg/m3)
Mass Ratio
(mrn/mr1= βi)
n=1
40
535.81
1
6.86x107
β1 = 1
6.05x10-12
β1 = 1
n=2
54.87
534.74
0.998
9.40 x107
β2 = 1.37
8.32x10-12
β2 = 1.37
n=3
69.74
534.28
0.997
1.19 x108
β3 = 1.74
1.06 x10-11
β3 = 1.75
n=4
84.61
534.05
0.997
1.45x108
β4 = 2.11
1.29 x10-11
β4 = 2.12
n=5
99.51
533.91
0.997
1.70 x108
β5 = 2.50
1.51 x10-11
β5 = 2.50
125
Table 5-2: Performance comparison of the three resonator array-composites in Fig. 5-6.
Array Mass
Ratio
(mMckt/mro)
Array
Stiffness
Ratio
(kMckt/kro)
Array
Damping
Ratio
(cMckt/cro)
(ηMckt/ηro)
(a)
8.74
8.74
1.0774
(b)
8.74
8.74
(c)
5
5
Array
#
Array
Coupling
Ratio
Array Q Ratio
(QMckt/Qo)
Array
Impedance
Ratio
(RMckt/Ro)
1
8.11
1.0774
2.56
2.5
3.50
0.41
1.04
1
4.81
1.04
5.2.3 Variation in Coupling Locations
The above analysis assumes all array coupling ratios, ηc, to be identical. This section
discusses the possibility of achieving a Q-boosting factor by leveraging ηc values.
This is true when the locations on the resonator where the two coupling beams are attached to
share the same stiffness. Close examination on the circuits in Fig. 5-5(b) reveals that the modifier
on the values of each circuit element, (N-1), can be absorbed to one of the transformer turn
ratios, ηc, without changing the electric response of the circuit. The resulting electric circuit is
shown in Fig. 5-8(a) with
c2
 N 1
 c1
(5-19)
As discussed in Chapter 1, ηc value greater than unity can be achieved via low-velocity
coupling, where the resonators are coupled at locations with lower velocities than the maximum
velocity. Such coupling scheme has been implemented with notched supports and been applied
to filters for achieving smaller bandwidth without further scaling the coupling beams [11][12].
Fig. 5-9(b) represents one possible implementation of such a Q-booting mechanical circuit
corresponding to the electric circuit in Fig. 5-8. Compared to the mechanical circuit in Fig. 5-
lx,1 cx,1 rx,1
1 : ηc1
cc cc
ηc2:1
lx,2
cx,2
rx,2
ηo:1
1 : ηi
-2cc
Co
Co
Fig. 5-8: The electrical circuit has the same electrical response when the values of ηc2 and ηc1
follow the relationship in (5-19).
126
Nodal
Line
Nodal
Line
(a)
(b)
Fig. 5-9: (a) the electrical circuit has the same electrical response when the values of ηc2 and ηc1
follow the relationship in (5-19); (a) the corresponding mechanical circuit when ηc2 = ηc1, which
is equivalent to the circuit in Fig. 5-5(b) with N = 2; (b) a possible implementation of the circuit
in Fig. 5-8(a) using low-velocity coupling on the electrode-less resonators, achieving ηc2 > ηc1.
9(a), the array-composite resonator with low-velocity coupling to the higher-Q resonator
occupies the same layout area but can achieve higher Q-boosting factors. Design on the coupling
locations offers is an efficient way to further reduce the layout footprint of Q-boosting circuits.
5.3 EXPERIMENTAL RESULTS
5.3.1 Fabrication of AlN Q-Boosted Composite-Array
Q-boosting wine-glass disk array-composite resonators were fabricated via the process
summarized in Fig. 5-10, which features 1.5µm-thick AlN structural material, 120 nm thick Al
top and bottom electrodes, electroplated Ni anchors, and the use of Mo sacrificial layers removed
via dry XeF2 etching. The material set and the fabrication steps used here are similar to those
described in Chapter 4. The differences worth-noting are listed below:
1. The lithography performed in step (3) and step (5) both use G-line photoresist and CD-30
developer, as most metal-free developer solutions suitable for CMOS and MEMS
processes contain TMAH which attacks Al.
2. The Al bottom electrodes are patterned via wet etch in OPD 4262, a TMAH baseddeveloper. Highly-selective wet etch is preferred over dry etch here to maintain a smooth
surface at areas without bottom electrodes, on which the AlN film will form the Qboosting resonators. Surface roughness is essential for proper c-axis orientation of the
AlN film sputtered later on in the process. Although the AlN film in Q-boosting
resonators is not responsible for energy conversion and its d31 coefficient is not critical to
device performance, experimental results have shown that resonators made of AlN films
with smaller FWHM peak of XRD measurement (i.e., better c-axis orientation) tend to
achieve not only larger coupling but also higher Q.
3. The Al top electrodes are patterned via RIE with chorine based chemistry and the etch
127
stops on AlN. Wet etch is not convenient here, as most etchants that etch Al also attack
AlN. While minimizing the roughness of the top surface of AlN film may be helpful for
achieving higher resonator Q, it is not as critical as the smoothness requirement of the
substrate prior to AlN sputtering.
(a-1)
(b-1)
(c-1)
(1) Deposit isolation layers SiO2/SiN; lift-off Al/Ni as the ground electrodes, interconnect, and
bond pads.
(a-2)
(b-2)
(c-2)
(2) Sputter and pattern sacrificial Mo via wet etch.
(a-3)
(b-3)
(c-3)
(3) Sputter and pattern bottom Al electrodes via wet etch;
(a-4)
(b-4)
(c-4)
(b-5)
(c-5)
(4) Sputter blanket AlN.
(a-5)
(5) Sputter and pattern top Al electrodes via dry etch.
Fig. 5-10-1: Fabrication process flow using cross-sections from the (a) disk, and (b) and (c)
anchor areas, explicitly showing the electrical contact between the electroplated Ni anchor and
the bottom and top Al electrodes, respectively.
128
(a-6)
(b-6)
(c-6)
(6) Sputter 20 nm thick Mo as barrier layer before PECVD oxide.
(a-7)
(b-7)
(c-7)
(b-8)
(c-8)
(7) PECVD oxide at 300 °C.
(a-8)
(8) Pattern oxide mask via dry etch; the etch stops on the Mo barrier layer.
(a-9)
(b-9)
(c-9)
(9) Dry etch Mo barrier layer with O2/Cl2/CHCl3 mixed gases; the etch stops on AlN.
(a-10)
(b-10)
(c-10)
(10) Dry etch AlN with Cl2/Ar/CHCl3 mixed gases; the etch stops on the first sacrificial Mo
layer.
(a-11)
(b-11)
(c-11)
(11) Sputter 20 nm thick Mo layer to electronically connect the entire wafer for electroplating in
the next step.
Fig. 5-10-2: Steps 6 to 11 of the fabrication process flow.
129
(a-12)
(b-12)
(c-12)
(12) Pattern thick photoresist; dry etch Mo within the trenches to expose the underlying nickel
layer as seed layer for electroplating.
(a-13)
(b-13)
(c-13)
(13) Electroplate nickel upward from the bottom Ni seed layer to fill the trenches as conductive
anchors.
(a-14)
(b-14)
(c-14)
(b-15)
(c-15)
(14) Strip thick PR in oxygen plasma.
(a-15)
(15) Dry etch the thin Mo layer and the remaining oxide hard mask.
(a-16)
(b-16)
(16) Release in XeF2/N2 mixed gases.
Fig. 5-10-3: Steps 12 to 16 of the fabrication process flow.
130
(c-16)
Fig. 5-11(a) and (c) present the microscopic images of the resulting structures in step (5) with
photoresist patterns and before Al dry etching. The electrodes are patterned such that each
anchor provides electrical access to either the top or the bottom electrode. For ring resonators
each supported by a single anchor at the center, 2-resonator arrays are used such that each anchor
electrically connected to the top and bottom electrodes, respectively, as shown in Fig. 5-11(c).
For wine-glass disk resonators with two anchors at two of the four quasi-nodal points of the
wine-glass mode shape, shown in Fig. 5-11(b), each anchor is connected to either the top or the
bottom electrodes. All of the bottom electrodes are electrically connected to the grounding
electrode of each resonator to prevent undesired electrodes between the bottom and grounding
electrodes. Grounding electrodes also apply to resonators without top and bottom electrodes to
prevent undesired electrostatic forces caused by dielectric charging on either AlN or the isolation
dielectric layers. Fig. 5-11(c) presents the microscopic image of a ring resonator array after step
(5), with clear distinguishment of the resonators with and without electrodes.
Electrical Access to
the Top Electrode
the Top Electrode
the Top Electrode
Photoresist
Pattern of Top
Electrodes
Grounding Electrodes
Grounding Electrodes
of Q-Boosting Res.
of Q-Boosting Res.
Photoresist Grounding Electrodes
Pattern of Top of Q-Boosting Res.
Electrodes
Patterned
Bottom
Electrodes
Patterned
Bottom
Electrodes
(b)
the Bottom Electrode
(a)
(c)
Fig. 5-11: (a) and (b) show microscopic images of Q-boosting ring and wine-glass disk resonator
array-composites, respectively, after step (5) in and before removing the photoresist; (c) an
array-composite similar to the one in (a) after the photoresist is removed, clearly showing the
electrodes only on certain resonators while the others are electrode-less.
131
Fig. 5-12 presents SEM’s of a 125-MHz version using four disk resonators, each supported
by two support beams attached at quasi-nodal points of the wine-glass mode, and all
mechanically coupled to one another via half-wavelength coupling beams. Fig. 5-12(a) and (c)
present zoomed-in views on an electrode-equipped and an electrode-less resonator, respectively.
For each electrode-equipped resonator, Ni anchors provide electrical access to the electrodes, one
connecting to the top electrode and the other to both the bottom and ground plane electrodes.
Ground plane electrodes are also used in the electrode-less resonators to prevent charging of their
AlN films during electrical measurement. Fig. 5-12(d) zooms-in on the edge of an electrode-less
resonator, showing the disk suspended above the substrate after release.
Fig. 5-13 presents SEM images of fabricated AlN Q-boosting array-composites. For each
array-composite, there is one electrode-loaded resonator on each end, which is coupled to
various numbers of Q-boosting resonators between them. The largest array contains thirty Qboosting resonators. Overhanging bridges made of Al/AlN/Al film stacks and supported by
electroplated nickel posts, shown in Fig. 5-13(f), helps simplify the interconnection of such large
mechanical circuits.
Electroplated Ni
Anchor
Top
Electrode
Grounding
Electrode
Coupling Beam
Etch
Residuals (b)
(a)
1.5 µm AlN
Disk
1 µm
350 nm Gap
20µm
Support
Beam
Coupling
Beam
41µm Long
1.5µm Wide
(c)
Fig. 5-12: SEM images of fabricated AlN Q-boosting resonator array-composite: (a) electrodeloaded resonator; (b) zoomed-in view on the edge of a disk resonator and (c) electrode-less
resonators.
132
N=2
Electrode
Electrode
(a)
Electrode-Loaded
Resonator
Input
GND
GND
Output
Electrode-Loaded
Resonator
N=4
GND
GND
Electrode-Less Resonators
(b)
N=8
(c)
N=12
(d)
N=16
(e)
N=32
Electroplated
Ni Pillars
Single
Line 1
Single
Line 2
(f)
Fig. 5-13: (a)-(f) Fabricated AlN Q-boosting array-composites each with two electrode-loaded
resonators and number of electrode-less (Q-boosting) resonators ranging from 0 to 30. (f) also
shows the zoomed-in views on the interconnect bridges used to implement more complicated
mechanical circuits.
133
5.3.2 Electrical Measurements
The Q-boosting resonator array-composites were measured using the setup in Fig. 5-14(a),
where the chamber pressure is 3 mTorr. The input signal is applied to the top electrode on one of
the electrode-loaded resonator and the output currents are collected from the top electrode on the
other electrode-loaded resonator. As AlN has low electrical conductivity, the output port is
electrically isolated from the input port, resulting in minimum feed-through currents. The two
electrode-loaded resonators are placed at the two ends of the array-composite to further minimize
the feed-through currents capacitively coupled from the isolation layers and the substrate. Unlike
electrostatic resonators, no DC bias is required to actuate the piezoelectric resonators. However,
DC bias can be useful to tune the frequencies of individual resonators to possibly reduce the
spurious modes and maximize the output power if large frequency differences occurred from
fabrication process variations. Furthermore, all of the bottom and ground electrodes are grounded
to prevent vertical electrostatic forces that can pull the resonators down to the substrate.
GND (DC = 0V) Network Analyzer
(Po = -5 dBm)
Bias-T
GND (DC = 0V)
Bias-T
Chamber
Pressure
= 3 mTorr
Output
Input
GND
GND
(a)
AlN
GND
AlN
Nitride/Oxide
Isolation Layers
(b)
Fig. 5-14: (a) Measurement setup for Q-boosting resonator array-composites, where the input
and output ports are electrically isolated for minimum feedthrough currents; (b) all of the
grounding electrodes and bottom electrodes are properly grounded to prevent vertical
electrostatic forces that may pull resonators down to the substrate.
134
Fig. 5-15 presents measurement results using the scheme of Fig. 5-14(a), where the top
electrodes of the left and right end resonators serve as input and output ports, respectively, and
all bottom and ground plane electrodes are grounded. Before Q-boosting, an array comprising
two electrode-equipped resonators exhibits a measured Q = 1,755 (Fig. 5-13(a)) that is lower
than previous work [3], probably due to etch residuals at the AlN/Al interfaces that are visible in
Fig. 5-13(b). Nevertheless, as shown in Fig. 5-15(b)-(f), as the number of Q-boosting electrodeless resonators in the array-composite increases, its Q increases, reaching as high as 10,444 for
the 32-resonator circuit, shown in Fig. 5-15(f), which is the highest measured so far for any
resonator constructed in sputtered thin-film AlN. The peak height changes very slowly as the
number of resonators is increased, confirming that impedance is not impacted until QMckt is on
the order of that of the high-Q resonators. Table 5-3 summarizes these measurement results.
Although the piezoelectric work in Chapter 4 demonstrates higher Q by lifting off the
electrodes from the resonator body to eliminate the electrode losses, the etch residuals in the gap
spacing possibly reduce Q and prevent the resonator from revealing the material Q of the AlN
material. The electrode-loaded resonators in this work suffer from similar metal contamination
issues, where etch residuals appear on the edges of electrode-loaded disks where electrodes
remain. This issue arises from direct etching of metal and AlN film stacks. Electrode-less
resonators, on the other hand, remain clean and free from etch residuals after release and can be a
better way to tap the material Q of AlN without the influence of electrodes and etch residuals.
Fig. 5-16(a) plots measured data of QMckt alongside the governing equation for QMckt given by
(5-11) with the number of electrode-equipped resonators ne=2 and with the Q of electrodeequipped resonators Qo = 1,755. All measured data points are clearly bounded by curves
generated when assuming electrode-less resonator Q of QAlN=14,040 (i.e., α = 8) and
QAlN = 15,795 (i.e., α = 9) in (5-5), suggesting that the Q of an electrode-less AlN resonator is
somewhere between these values, and confirming that AlN is capable of achieving high-Q (Q >
10,000) when metal electrodes are not present. The Q of the electrode-less resonators affect not
only the measured QMckt but also the impedance, RMckt. Similar procedures can be applied to
extrapolated QAlN by plotting measured data of RMckt alongside the governing equation for RMckt
given by (5-12), as shown in Fig. 5-16(b). This approach gives the same range of QAlN as using
the QMckt data.
Table 5-3: Summary of measurement results of various Q-boosting resonator array-composites.
Total # of Total # of Q-Boosting
Measured
Res., n
Res., ne
Array Q, QMckt
2
4
8
12
16
32
0
2
6
10
14
30
1,755 = Qo
3,162
5,167
6,264
7,711
10,444
135
Q-Boosting
Measured
Factor
Array R, RMckt
(QMckt/Qo)
1
3137
1.8
3545
2.9
4360
3.6
5175
4.4
5990
6.0
9249
Impedance
Ratio
(RMckt/Ro)
1
1.13
1.39
1.65
1.91
2.95
N=2
Q = 1,755
Q = Qo
S21 (dB)
-40
-50
-60
-70
-30
N=4
Q = 3,162
= 1.8·Qo
-40
S21 (dB)
-30
-50
-60
-70
-80
-80
-90
-90
121 122 123 124 125 126 127
121.5 122.5 123.5 124.5 125.5 126.5
Frequency (MHz)
Frequency (MHz)
(a)
N=8
Q = 5,167
= 2.9·Qo
S21 (dB)
-40
-50
-60
-70
-30
-50
-60
-70
-80
-80
-90
-90
122.5
123.5
124.5
125.5
124
Frequency (MHz)
-60
-70
-30
-30
-40
-40
S21 (dB)
S21 (dB)
-50
-70
-70
-80
-80
-90
-90
-90
123
123.5
127
124
N = 32
Q = 10,444
= 6.0·Qo
-50
-50
-60
-60
-80
122.5
126
(d)
N = 16
Q = 7,711
= 4.4·Qo
-40
125
Frequency (MHz)
(c)
-30
N = 12
Q = 6,264
= 3.6·Qo
-40
S21 (dB)
-30
(b)
124.5
124.8 125 125.2
124.8
125.2 125.4
125.4 125.6
125.6 125.8
125.8
Frequency (MHz)
Frequency (MHz)
(e)
(f)
Fig. 5-15: Electrical measurement results of Q-boosting resonator array-composite of various
numbers of Q-boosting resonators in the array.
136
11
Qo = 1,755
QAlN = 15,619.5
QMckt
9
7
Qo = 1,755
QAlN = 13,513.5
5
Measurements
3
1
0
5
10
15
20
25
30
35
# of Total Resonators n
(a)
10
9
Qo = 1,755
QAlN = 15,619.5
RMckt (kΩ)
8
7
6
Qo = 1,755
QAlN = 13,513.5
5
4
Measurements
3
0
5
10
15
20
25
30
35
# of Total Resonators n
(b)
Fig. 5-16: Plots of theoretical prediction and the measured data of resonator array-composite
with different numbers of Q-boosting resonators to extrapolate QAlN (a) using and the measured
data of QMckt; (b) using and the measured data of RMckt.
137
5.4 Conclusions
Via use of a Q-boosting mechanical circuit, array-composite resonator Q as high as 10,444
has been achieved, and curve-fitting reveals Q = 14,040~15,795 for electrode-less AlN
resonators — more than 8 larger than the Q=1,755 of electrode-equipped versions. These
numbers confirm that AlN itself is indeed a high Q material and losses associated with
electrodes, not the material, are most responsible for the lower Q historically measured for AlN
resonators. The Q-boosting method demonstrated here further constitutes an attractive approach
to achieving the simultaneous high Q and strong electromechanical coupling sought by many
emerging applications, such as RF channel-selecting communication transceivers. The method’s
ability to boost Q is certainly extendable to other piezoelectric materials, such as ZnO and PZT,
and even higher Q should be possible if piezoelectric resonators can be coupled to resonators
constructed of higher Q materials, such as poly-crystalline diamond [13].
5.5 References
[1] J. Wang, J. E. Butler, T. Feygelson, and C. T.-C. Nguyen, ―1.51-GHz polydiamond
micromechanical disk resonator with impedance-mismatched isolating support,‖ in Tech.
Digest, Int. IEEE Conf. on Micro Electro Mechanical Systems (MEMS’04), 2004, pp. 641644.
[3] G. Piazza, P. J. Stephanou, and A. P. Pisano, "Piezoelectric aluminum nitride vibrating
contour-mode MEMS resonators," J. Microelectromechanical Systems, vol. 15, pp. 14061418, 2006.
micromechanical wine-glass disk oscillator,‖ Technical Digest, IEEE Int. Electron Devices
Mtg. (IEDM’05), 2005, pp. 287-290.
[5] R. Tabrizian, M. Rais-Zadeh, and F. Ayazi, ―Effect of phonon interactions on limiting the
f·Q product of micromechanical resonators,‖ Dig. of Tech. Papers, Int. Conf. on Solid-State
Sensors & Actuators (Transducers’07), 2007, pp. 2131-2134.
[6] L.-W. Hung, and C. T.-C. Nguyen, ―Capacitive-piezo transducers for higher Q contourmode AlN resonators at 1.2 GHz,‖ Solid-State Sensor Actuator Workshop, Hilton Head,
2010, pp. 463-466.
[7] L.-W. Hung, and C. T.-C. Nguyen ―Capacitive-piezoelectric AlN resonators with Q >
12,000,‖ in Tech. Digest, 24th Int. IEEE Conf. on Micro Electro Mechanical Systems
(MEMS’11), 2011, pp. 173-176.
[8] L.-W. Hung, and C. T.-C. Nguyen , ―Q-boosted AlN array-composite resonator with
Q>10,000,‖ Technical Digest, IEEE Int. Electron Devices Mtg. (IEDM’10), 2010, pp. 162165.
138
[9] Y.-W. Lin, L.-W. Hung, S.-S. Li, Z. Ren., and C. T.-C. Nguyen, ―Quality factor boosting via
mechanically-coupled arraying,‖ Dig. of Tech. Papers, Int. Conf. on Solid-State Sensors &
Actuators (Transducers’07), 2007, pp. 2453-2456.
ring resonators," in Tech. Digest., 17th IEEE Int. MEMS Conf., pp. 821-824, 2004.
[11] F. D. Bannon, J. R. Clark, and C. T.-C. Nguyen, ―High-Q HF microelectromechanical
filters,‖ J. Solid-State Circuits, vol. 35, no. 4, pp. 512–526, 2000.
[12] S.-S. Li, Y.-W. Lin, Y. Xie, Z. Ren, and C. T.-C. Nguyen, ―Small percent bandwidth design
of a 431-MHz notch-coupled micromechanical hollow-disk ring mixer-filter,‖ Proceedings,
IEEE Int. Ultrasonics Symposium, Sept. 18-21, 2005, 1295-1298.
[13] J. Wang, J. E. Butler, T. Feygelson, and C. T.-C. Nguyen, ―1.51-GHz nanocrystalline
diamond micromechanical disk resonator with material-mismatched isolating support,‖
Proceedings, 17th Int. IEEE Micro Electro Mechanical Systems Conf., Maastricht, The
Netherlands, Jan. 25-29, 2004, pp. 641-644.
139
Chapter 6: Conclusions
6.1 Achievements
The work presented in this dissertation successfully demonstrates four new approaches to
improve the performance of both capacitive and piezoelectric resonators. Specifically, two new
approaches are demonstrated to facilitate fabrication of gap spacing on the order of 20 nm. Such
small gap spacing is the most efficient way to improve the coupling efficiency of capacitive
transducers and to reduce the impedance of capacitive resonators. Another two approaches aim
to improve the Q of piezoelectric resonators by eliminating the losses associated with contacting
electrodes common used for piezoelectric resonators. Although this work targets at applications
for wireless communication, other applications which require unconventional microfabrication
techniques, capacitive transducers, or piezoelectric transducers are likely to benefit from the
results of this work as well.
Conventionally there are three ways for forming suspended microstructures: wafer bonding,
anisotropic etching, and release etch. While wafer bonding can achieve ideally unlimited aspect
ratio, it is usually not a cost and layout area efficient process. Whenever there is an etching step
involved in the release process, the mass transportation rate and the etch selectivity together limit
the maximum achievable aspect ratio of the microstructure. Instead of directly etching a small
gap, ALD partial-gap filling was used to reduce the gap spacing from 97 nm to an effective gap
spacing of 32 nm, resulting in 7x increase in the coupling coefficient. Even with Q reductions
caused by partial-ALD-gap filling that in turn result in Rx‟s only 2.7X better than those of larger
air gap devices, the impact of this work is still enormous. This impact is perhaps best gauged by
considering the effect of partial-ALD-gap filling on the demonstrated differential disk array filter
of [1]. Here, a reduction in gap spacing from 80 nm to 32 nm of the resonators used in this
micromechanical circuit would reduce the needed filter termination resistors RQ from 2.8k to
only 72, which is now compatible with present-day board-level impedances. Since the Q‟s of
the radial-mode disk resonators used in the work of [1] were only 10,500, the Q of 10,510 of this
work can maintain the same low insertion loss of 2.43 dB for 0.06 % bandwidth performance of
that filter, but with much smaller matching impedances. Work to actually demonstrate such a
filter using partial-ALD-filled gaps is in progress.
Another approach, silicide-induced gaps, removes the etching entirely from the release
process. By utilizing a volume shrinkage-based method for forming gaps between structural
layers and thereby avoiding the need for etching, the silicide-based release process demonstrated
in this work is cheaper, cleaner, and faster than conventional etch-based methods, as it requires
no etching, consumes no chemicals, and has little dependence on mass transport processes. This
is the first time that silicide is used to form internal gaps and to release microstructures. As the
required annealing time is independent of the lateral dimension of the devices, this method can
form internal gaps by annealing the device for only seconds or a few minutes, compared to tens
of minutes or even hours required by etch release. For example, using this method, structures
with aspect-ratios exceeding 260:1 have been released in less than two minutes—substantially
140
less than the 40 minutes otherwise required by an etch-based release process. A titanium beam
resonator released by silicidation is demonstrated to confirm the efficacy of this approach
applied to a real application. The type of metal and semiconductor material used, the annealing
conditions, the phase of the silicide formed, and the thickness of the metal together determine the
final gap spacing. By sputtering thinner metal films, gap spacing as small as 32 nm is achieved.
Furthermore, nickel silicide formed at less than 350 °C can be used for applications that have
thermal budget constraints.
Piezoelectric resonators have conventionally been measured to show lower Q than capacitive
ones. Therefore, there is a common belief that AlN sputtered at low temperatures is not a high Q
material. The measurement results of both the capacitive-piezoelectric resonators and the Qboosting AlN resonator array-composite confirm that losses associated with the electrodes are
more responsible for the lower Q measured before.
The first approach eliminates the losses associated with the electrodes by separating the
electrodes from the resonators. As the electrodes no longer mass loading the resonators, even
thicker electrodes can be used to reduce the resistive loss, therefore higher Q. This scaling
advantage is especially when smaller lateral dimensions of the resonators and the support beams
are required for higher resonant frequencies. The coupling coefficient is a function of the gap
spacing; the smaller the gap spacing, the larger the coupling coefficient. Unlike the ~ 20 nm
requirements on the capacitive transducers for narrow-band filters at GHz frequencies,
capacitive-piezoelectric transducers require no smaller than ~ 100 nm gap spacing, which can be
achieved with conventional sacrificial material etching. A 1.2-GHz capacitive-piezoelectric
contour-mode AlN ring resonator achieve a motional resistance of 889 Ω and Q = 3,073,
confirming that resonators equipped with “capacitive-piezo” transducers can achieve higher Q
than so far measured for any other d31-transduced piezoelectric resonator at this frequency and at
the same time maintain high electromechanical coupling. Further, by applying capacitive-piezo
transduction to separate a 50-MHz AlN two-disk array-composite resonator from its electrodes
by nano-scale gaps, a Q as high as 12,748 has been measured, which is the highest measured so
far for any AlN resonator. The results of this work experimentally confirm theoretical predictions
that AlN is a high Q material, capable of achieving the Q >10,000 needed for some RF channelselect wireless communication front-ends. They also confirm that it is most likely electrode loss,
not material loss that dictates the lower Q‟s previously measured for AlN resonators with
contacting electrodes. Given evidence that anchor losses probably still dominate the Q‟s of the
devices used in this work, it would not be surprising if future use of capacitive-piezo
transduction in more effective anchor-isolating designs yields devices with even higher Q‟s.
The last part of this work also sets out to prove that sputtered AlN is a high Q material. Qboosting mechanical circuit consists of electrode-equipped and electrode-less resonators coupled
to each other via half-wavelength coupling beams. Electrode-equipped resonators provide high
coupling coefficients but lower Q while the electrode-less resonators can achieve high Q but are
not involved in the energy conversion process. Via use of a Q-boosting mechanical circuit, where
the energy stored in the higher Q resonator is shared with the lower-Q resonators, the overall
array Q is „boosted‟ to be higher than the Q of the electrode-equipped resonators. A Q-boosting
AlN array-composite resonator Q as high as 10,444 has been achieved, and curve-fitting reveals
Q = 14,040~15,795 for electrode-less AlN resonators — more than 8 larger than the Q=1,755
of electrode-equipped versions. These numbers confirm that AlN itself is indeed a high Q
material and losses associated with electrodes, not the material, are most responsible for the
141
lower Q historically measured for AlN resonators. The Q-boosting method demonstrated here
further constitutes an attractive approach to achieving the simultaneous high Q and strong
electromechanical coupling sought by many emerging applications, such as RF channel-selecting
communication transceivers.
6.2 Future Research Directions
The work presented in this dissertation successfully implemented four new techniques to
achieve high-Q and low-impedance micromechanical resonators by either fortifying the
electromechanical coupling of capacitive resonators or enhancing the Q of piezoelectric
resonators. These techniques are useful for capacitive and piezoelectric transducers and forming
high-aspect-ratio microstructures using microfabrication in general and, as a result, seed future
research.
As either capacitive resonators equipped with sub-50 nm transduction gap spacing or
capacitive-piezoelectric resonators with ~100 nm air gaps can achieve Q > 10,000 and sufficient
coupling, it is now possible to implement narrow-band and low-loss MEMS filters at GHz
frequencies. In particular, capacitive-piezoelectric resonators provide unique research
opportunities in the following directions:
1. Filters implemented with the capacitive-piezoelectric resonators do not suffer from
feedthrough currents and obsolete the need for differential operation to cancel the
feedthrough currents as capacitive resonators [1].
2. Oscillators implemented with the capacitive-piezoelectric resonators can possibly achieve
better far-from-carrier phase noise than capacitive ones due to larger power handling
capability and maintain high Q, low impedance and high linearity necessary for
minimizing far-from-carrier phase noise low at the same time.
3. The capacitive-piezoelectric resonators are suitable for CMOS-MEMS integration. The
majority of the fabrication process for the capacitive-piezoelectric resonators
demonstrated in this work has process temperature less than 300 °C. The only exception
is the deposition of the isolation layers of low-stress nitride and thermal oxide, which are
chosen to minimize the surface roughness before the actual fabrication starts. When
integrated onto a CMOS chip, the intermediate isolation dielectric (ILD) layer followed
by standard chemical mechanical polishing (CMP) can replace the need for the current
high temperature deposition of isolation layers.
The silicide-induced gap is a method for releasing microstructures or forming internal gaps
that is fundamentally different than all of the conventional ones. This method can be applied to a
wide range of MEMS devices. On the other hand, more studies on material properties will help
the researcher harness the silicidation process. For example, while silicidation dynamics have
been studied for 30+ years, effects of silicide-induced gaps, where the capping layer imposes
non-trivial boundary conditions on the reactive diffusion, is new to the field. To experimentally
verify a proposed model, samples of various silicides can be in-situ annealed during X-ray
diffraction measurements, which will reveal the progressive change in sub-surface film
composition.
142
6.3 References
[1] S.-S. Li, Y.-W. Lin, Z. Ren, and C. T.-C. Nguyen, “An MSI micromechanical differential
disk-array filter,” Dig. of Tech., the 14th Int. Conf. on Solid-State Sensors & Actuators
(Transducers‟07), Lyon, France, June 11-14, 2007, pp. 307-311.
143

High-Q Low-Impedance MEMS Resonators

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